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1987
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517.43
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B cB.flBrr c pasBrrrr4eM Henoropblx paBAeJIoBrrpr4niraAHoro aHaJIrrEa vI.,
trperfiAe Bcero, cy6gu$SepenrlrraJrbrroro ucqucileHr4fl B rrocJreArrrreroAbr BaMerno Bbrpoc IluTepec r(o BcgMy ctrenTpy rorroirorr{qecnrrx uoHsruft, 6ruaftux
R rretrpepbrBrrocrrr.O6aop rroAXoAoBIt rrocrpoeHr4rou nayqeHrrro KacareJrbrrbrx
rra ocHoBe r(orrcrpyxqufi Tr4rraBepxuux trr lrll?nnrrx [peAeJIoB rrocJreAoBaTeJl:buocreft Muolnecrts Aarr III. fioneqnrrM u [t]. B [2] ]It.-fI. fleso BtseJrrroHnrurr
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crarbrr - rroftaaarr a$$enTrrBHocrb cpeAcrB HecrauAaprrroro aHaJrrraan a'roft
npo6neuarrrxe. B pa6ore ycrarraBJrlrBaercfl o6rquft Sanr, yrur$nqnpyrorqnft
.trBbrnoBblecpeAcTBa, y[rorpe6rneurre npv accJreAoBaurrrrcBoficlB, poAcrBerrEbrx He,trpepbl,Buocrra.
Ha arofi ocuo'Be BbrBoA.flTcguonrre npuauaxr.r HoMrran'rtrocrtr Sunrrpon, cy,6neupepbrBuocrr,r,
npeAeJroBcoorBercrnrafi, a ran)fie Aaorcfl, rrpocrble HecrarrAaprubre AoxaaareJrbcrBau oSo6uleuun Henoropbrx cBflBarrrrbrx c r{r4MrryrBep}r(Aenvrfr.ua [3, 4].
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1.0. B eroM uaparpaSe co6panrr neo6xoAr{MbleBctroMorareirbHbrecBef,euua, fiacarcqrrec.fi r(c[oJrbaoBaHtrfl rrecraHAap'Trrbrxcpe4crB B Teoprrn dxtlrTpoB. OrsocureJrbrro 4eraneft_MoHaAoJrorrrucr{. [5, 6]. llcuonraye,urrft rroAXoA
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Wg)
9. Ecnu fi crryxtrtr 6asflcoM
BHemEee Mrrox(ecrBo crarrAaprubrx DJIeMeHTos
q,,
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ro
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crarr,qaprHa (u, crano 6nrrr, u'cxo'ArrbrftSunrrp cocraBJlen Bce,MI{HaAMHo}r(ecrBaMa csoefi lrouagrr)
a s X n Y u $vm.rp I B aA eB aer
l. 2. f ly c t r
I cX XY -c o o rB e rc rts r,re
qro ro ?fiecaMoe,p(g) 0 dom f *
dom I, r. e. (vF e g)F l'l dom T'+ g urJrvr,,
,+ g. Paccuorpuu o6paa | (g) fiutarpa F,, aagannnft cooruorueHr{en
T (g):: lG c Y: (sF = g)G = f (F)).
Moaa1a o6paaa ecrb o6paa wou,a1at,r. e.
p (f (.r) ): f hr@) )
(agecr ucrroJrbayercfl.crrJrbnarr{opua rptrHrlura rrAeaJrrraaqun).
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Muo?fiecreo.
.
B coorseTcrBrra c nprrHql4rroMrrAeaJltraaqrrr4
B E ranerorc.flBHyrpeHHrre a.JreoE.
MeHTbr, Ma?fioprrpyroqae
Vlx rraabr,Barory1a,rteruu,otuuvrrt 6ecrcone,tno
6o",tautuuu s E. - Paccuorpuu cran'4aprnsrfi 6aaprc {lrnr,rpa xBocroB fi ::
t:{o ( E ) :
E eE } , rx e o -tro p fl A o i n B E. fl u ro , qro Mo} ra4aS unrrpa xB ocroB
150
C. C. Ityrarena|ae
cocTaBJlerratr3 yAaJrerrHbrx SJIeMeHToBpaccMarptrBagMoro HatrpaBJre:Hvrfr.
vlctronbayror Ba,rrr{crr"E :: p(g) n E x f oo.<--+E = '8.
H & n p a 6 . f t e l d u r ,E : : E ( . ) :
1.4. Ilycra E, H-1ea
f{+E-nenoropoe
or o 6p ailcen ue. .9n,eu ea.oeHTIrbL ct e0y rcu4ue Ar 6ep uc0emua:
(1) E('H)coE;
( 2 ) ( v E= E ) ( s q e H ) ( Y q '> T t ) E( q ' ) > € .
{.8 caMoM AeJIe, (t) osHaqaer, qro Sranrrp xBocroB E rpy6ee o6paaa
Sunrrpa xBocroB H, T. e. rrro B Kalr(AoMxBocre HarrpaBJreuzgE JreE(r{To6paa
Hexoroporo xBocra H. flocne4nee yrtseplr(Aerrrren cocraBJrfler coAep)fianue
(2).
1.5. flpt
ycnonraft 1.4(l), L.4(2\ roBoBbrrroJlHerlurrenBr4BaJrerrrubrx
pf lr , qr o H - n o } u ,a n p a e a e n u eE (o ru o c n reJrbnoE (.) )
1 . 6 . f l y c r r X - H e n o r o p o eM H o ? f i e c r Bro4 r i : r ( . ) :
E*X-rrexoropafi
cerb arreMeHrosx (uraurelr TaKlr(e (15)6== rrJrr4rrpocro ("u) ). flycrr, AaJree,
( y r ) n= t t - er qe o A H a c e rb a J re Me n ro BX . f onopnr, qro (A r\-no7ceru MA pa
cerr4 (r), vrla crpoeaa no7cera (r), ecJrrr"
H .ssn.sercfl rro4narrpaBJreuueivr
E
o T B o c I { T e J I bTHaoK o r o[ ( . ) , u t o U , t : r E . ' 4 t r r p f i B c e x q e H ,
T. e.A:r"E.
Ifoguepn1eu, rrro B crdrryI.2 nsuoJrrreHoy('H)-lr(:E).
1.7. flocneAHee yKaBaHHoecnoricrso uo,trcerefi Mypa roJro)fieuo e [7] n
ocuoBy 6onee cno6o4uoro onpeAeJreHrrflrroAcerrd,Koropoe [pr{BJrenaeT HerrocpeAcrBeHnofi cBflBbro c Sra"urrpaun, a rrMeHHo: cerb (yr)n=n BJreMeHTo,B
X
uaabrBarorno)cerorc (wnm no1ceraro 6 wuponott, cMbl,crlecrloea) cern (16)6=e
areMeHTonX, ecltt
( v E= E ) ( u q = H ) ( v r l ' 2 r i ( s E ' > E ) r ( E ' l r : a ( \ ' \ ,
T. e. B cryrrae, KorAa narH4srft xBocT cerr{ r coAepffirrr Hefioropbrii *"oat y.
IIa gerrHe MoHaA, paayMeercfl, BbrrroJrueHoA (H) = r ('E\ 1 nilv. n nar;rn4noii
Sauucu '
(Yrl = *-) (trfi = +*)
Un: te.
llpn 3ToM, cTpeMflcb n o6paauocrra,qacro rrrrruyr: (rr) reH -rroAcerb cerr
(rs)s=" (vro Mo)fier rrpr{Becrrl r{ He.Aopaayueunarr).floneeso [oAqepnHyrb,
trro B o6Ir1er,rc.lryqae rrogcerrr ne o6.searrbrflBJrflTbcfl noAcer.flMr,rMypa. OrlreTr4r,rTaKlrte,qTo ABe ceTr{ B oAHoMMHo}r{ecTBe
HaSbrBaroTcfl
eq6u6aJreITTItblhnt,,
ecJrl4KairiAaa I,IBHrrx,- rroAcerb 4pyrofi, T. e. ecJrr{ rrxilroHaAbr coBfiaAarot[71.
1.8. Ecnu g - Sn.rrr,rpn X m (r)cerb EJreMeHroB
X,'ro rotsopflr, rrro
paccMarpr4BaeMaflcerb no}rruH,erdag rrpu ycrroBrrr4E = +o" -->rz=W(g\.
Tlna.re roBopfl, cerb (rs) no4ur4HeHa9, ecrt {tr"nrrp ee xBocroB ronbrrre 9.
flpu aroM Aorrycnaror BoJrbuocrb r/r rrr4rrryr rs I 9, rlMe.EB BrrAy aHaJrorrlro c
TorroJroruqecnl4Mno6oaHa.re'HrrflMncxoArrMocrr4.Orlrervlr BAecb HO, rITo B
cJry,qae,HorAa g - ynrrpaSrrJrbrp, F conua4aer c Slrnrrpou xBocrots nro6oft
iloAquueunori elry cerr{ (r). B .racrHocrr4, caMa ranafl cerb (r) - A,/Lbrpar
ceru l7f.
1.9. Teopewa. IIycrb q:g(r,
A, z)- fiop*y.lla reopuu Qepue"rto-@peru,ne,nfl. u,e co)eplffau4an vtunar{ur ceo6o0nblfr n&pamerpor,, npowe fr, U,, z, npuq , e n z - c r a n } - a p r v o e i l H o i l c e c r r o .I f y c r u , , ) a , n e e , g - $ u t o r p
6 X, a9$u,nurp e Y. Cte7yrou4ue yreepw?eHufl,enrurarteu,rnbl:
(1) (vG=9) (sF =g)(vref)
(sa eG)
c p ( r ,U , z ) ;
( 2 ) ( Y r e w ( g ) \ G a = p @ ))
q (*, a,r);
(3) 1tta ,nrc6oriceru (r5)6=e eJlemerr,ros
X, no}uunennofi 9, u,afi}yrca
cerb (yn)1=n eJlemeruTorY, no}rtuHerdH,aa9,, a crpo?an no}cera ("u,n,)n="
c er u ( r . ) . = = T a H rL eu) ro . n p u T c e fr n e H 6y0er g(/etnr, U n,z), T. a.' cui l I?ort)uqecwu
(Yre I g) (wyr I g)
I ( / e r n r ,U r , z ) i
(4\ O,nn nto6ofr, ceru (",),== eJleweltror X,, no}rauH,ewtofi,F, n'afi}yrca
c er b ( y r ) n= " e rL e w e H T o rY rn o 7 w u ru e ru n aa
9ru no)cera (" n)n= " ceru (" r)r-*
Talru,elaro npu 6cefr q e H 6y0er e(/n, An, z), r. e. cuwroJLuaecttu
( Y r e +g \ ( t y n l 9 )
e ( r n , U n ,z ) i
g, ,
. ^(5) O,na .no6ofi a.nbrpaceru (rs)6., erle-Merrror X,, no0,{uH,eH,t{,ofi,
u'ail7yrca Arlbrpa,cerb (g/q)n=u,no7uuruennaa'9, u AJLbrpacerb (rq),r=u, an6rr^Bh.neuTltan(re)e-=, rT,rf,u,e,,
HTo q(rr, ur, z) npu scer I e H:
crauAaprToro G rrMeercfl crarrAaprrroe F ra_xoe,
_qro (y r = F) (ga = G)
y(*, u, z). 3na'rrr, Ailn re p"(F) 6y4er (yGe "9) (sa'=G)
,pb, a, z)'.
flpuueHaa . npuHrlr,nr zAeaJrrma{trtr, BbrtsoAr{M
| (gi) (v G ='"9)' i ; G A
A P (q,a, z). trllun,a e w@) w e(r, a, z),
(2)t (3). Ilycrr (qe)Eee-- crarrAaprHa.flcerb n X, to,4qrrHerrHaxF.
$a?fiAbrxcraHAaprnrrx G ve I u Ee,E uonornuu
A ( r , 0' : { € ' } E :
( Y t "> E ' ) ( f l y = G )
f,na
c p ( n 8 , , .zA),) .
[Ia ocnoBaHl4uI.I n !.,2 tsr{ArrM,.rro oEcAp,Et. Vurarrr,naa, qro Arc.e,tBEyrperrHee Muolr(ecrBo,
Tg rrplu44uy rtorura safirroqaeM: "Aro,ur*@. Tenr
caMbIM rra HatrpaBJreHl{rr
H :: I XE _(c ecrecrBeHrrbrMyuopaAoueuuerlr) Ba--E v
Aarr.brcrarrAaprnrre oro6pax(_erlrrfl
E:_H
A: H--+ I ralHlre,qro E(n)=
t
p
y
.
G
e
g
a E e 8 , 4 n n H o t 6 p " r x \ : ( G ,\ , / E ) . B r n n " o , . i t o
?,Alr,et.n UneG
a A n = p @ ) n -p r q J + " " .
E ( ? 4 :). * (3) * (4). OuenrrAHo.
(4)* (1). Ec.nu (1) He Bbrrrorrueuo,ro rro ycJroBrrro
(nG e 9) (YF eg) (Er= F) (vU =G). arp(*, A, z)
nr r 6v p a e M rre F
ta n _ ,.Iro 6 1 16 rrn o 1rp(r, U ; z) Irpn B cex a= G.
W^ F ef
Orlteruu, qro [oryqaeMyro cerb (re)t,=g
EJTeMeHToB
X, paBHo KaH rd Mrro;
?fiecrBo G ltoxno cqrlTarb craHga'prHbrMpr
rra ocHoBan:aur[prrur{rrrra [epeuoca.
Her _c_ouueunf,r.
r'ro. re I F w, craJro 6rrrr, B crrJry (3) nafi4yrcn HarrpaBJrenze I! rr rloAcerb (r1)1=u cerrr (l.'p)r=g Tanrae,qro AJrfl
ceTrl
"enoropoft
(yn)r.tr 6_VRerg(rn, Ur, z\ rprr Kalr(AoMqeH. flo onpeAerrerruro'I.7
r, tpv
{a}r(AoM 6ecnoHe.rno6onruroM q coBtraAae'Tc r, AJr.flHexoroporo yAaJreggoro
F, r. a. rn=p(g).
f l o . y c J r o p r 4 rU
o n=W(9) rr reM 6onee Ar=C. flp, BroM
or(a3brBaercflg(rn, Ur,,z) u le (rn Un, z), uero 6rrrs
ro"lner. flolyuenrroe
"e
rrporrrBopelze cBrrAereJlbcrByeTo JrolnHocrr4 cAeJraHnoro
Aorryrqeulr.s. Tafi11]a
o6pasonr, (lL.mruoJrueFro (xan roJrbnorrMeer Mecro (4)).
(1) * (5). fiira AoxagarerlbcrBarpe6yemoft ansnsaJreHrrrocrfiAocraroqHo SaMerrrrb, qro ona crauoBr{Tcfl oqeBuAHoftn clyuae, HorAa F tt 9 cyrn
ynntpa{uJrbrpbr (cp. 1.8). Ocraercs BotroMHrrrb,qro na}fiAafl onotra4ae"cr"
o6se4raneHrreMoHaA ynrrparsrdJrbrpoB.
1.10. B upunorfieul4.flx 6uBaei y4o6nnrm paccMarprrBarb Korrxperrr3aqnr(
l.g, orBeqarcque crryqa.flM,B noropbrx o4"o ia Sunirpon 4rr.np6r.u. Tan,
uctroJlbay.fl ecTecTBeHrrbreo6oauase:r,wfl.1
tsbrBoArlM
(sr= p(g))
p(r, il*
( n r e +g )
q ( r e ,A ) ;
( Y r = W @ ) ) q ( t , y ) * ( y r E +g ) ( E r r + g )
q(rr, A).
$ 2. IlpeAenhr coorBercrsuft
2,0. B DToMnaparpafreco6paubrBcrroMorareJrbrrbre,
HaKtrpaBaJro,
rrBBecT-
Ebre cBeAeHIrff o IrpeAeJrax ceuefictn MHotfiecrB, uctroJrbayeMbreB ganrneftmeM. Orsocrrerrbto uglops_r4Borrpoca cu. [{, 8].'
2.1. IIygTb I c X xY - BHyrpeunee coorBercrBrre ns crarrAaprgoro
lrfEorfiecrsa x n craEAaprnoe Mno,fiecrBo Y, ,{ouycrult, qro B x'nrr4eneu
cranAaprnuft Slrnsrp 9,, a s Y-Torrojrorv.fi. -c.flouaraeu (cp.
[g])
vY(f ) ::*{A': (yre p,(g)ft doml) (vy x
A ' ) @ , U , ) el } ;
sY(I):=*{y':
(ore p(g)fl domf) (vy = A,) @, A)e f};
vs (I)::*{A':
( y r e p ( g ) f l d o mI ) ( s y - A , )
,
@, ile l};
*
{
A
'
:
s s (I) ::
;
(sr = p(g) fl dom f) (sy o U,) @,
ile I},
TAretaaSe
a Banrrcb A x A' o3Haqaer,
rAe, HaK o6rruno, * - cu.,\r'Boncr&HAapru3a.ryuu,,
q ro A € p( r ( A ' ) ) . N l n o m e c rB o Q ' Q r(I) H a abrB arorQ' Qr-npe0e.nonf (a4ecr
Q - oglru I{B r(BarrropoBV unn f, ).
2.2. B rorro,rroudrr o6rr.ruo orpanrlqrrrBarorcfi cryrraeM, KorAa I - cragAaprrroe coorBercrBr(e, onpeAeJreHrroeHa HenoropoM EJreMeHTe$ranr,rpa fr.
flpu arou r.Igyqalor flf,-npeAeJr lr YB-npegel. flepnnul HasbrBaror sepr.IruJtt,
npe1etto*t, a BTopofr.- ttutrcnuil, npe}e,non T e}o.na 9.
Ec;ru paccrrarprrBaercfl cerb (rr) r=" s o6racrlr oilpeAeJrenrrrrl, ro, rrMefi
B BrrAy tfu;rrrp xBocToBceTrr, rroJrararor
Yg (f ) ;
L s g = " I : : l i m s u P E = " | ( r r ), : g g ( f ) .
B ranux cJryqa.sxqaqe Bcero roBop.flr o npe7e,nar KyparoBcnoeo.
'2.3.
Aog. cranAaprnoro coorBercrBrrfl f clpaBeAJrrrtsbrrrpeAcraBJrenrTtr
Lis==I :: lim infs="I (tc)::
g[(r):
n cl U I(e);
,c€.F
Feg
Yg(I):
n cl U I('),
r=:ii
ccsF
,X" g - ETo ran HaabrsaeMrrft?pu,nb 9, T. e. ceueftcrBo, cocraBJleHHoeBcellnaqe roBop.fi,
Mtr troArruorfiecrBauu X, BaAeBarorqlrMlrMoHaAy p g).
h:*{F'e.X:
Orueruu
(vFc.F)
F, np(g)+g}:{F'cX:
F nF'+Al.
n grofi cBflBu coo'Tgolrrenufr.
gv(f):
U int n I(t);
tetii
,
VV(I):
x=F
U int n I(r).
le.F
xJF
2.3. lls reopeMbr 1.9 urnoBeHHo cJreAyer orrlrrcaulreilpeAenoB Ha .sBbIKe
eerefi.
2.4. 9,neJ]ueHT
U JLutcrLTB YT-npe1eae I 6 row u Torlbno roilt, crtAq'aer
9, u'afi1Vrcfl
ecrlu O.nana.rc7oil ceru (16)E,="eJleilevToa domT,, no}uurueruu,ofr,
nolcera ("n)n." ceTu (rg)g=a u ceTb (yn)n=n, cro1au4aaca fi A, TanII'e1q,To
(ro, v ) eT
O . na6 c e n 4 e H .
2.5. p.neileH,TA Jreilcur 6 ET-npe}ete I 6 ToJw,u rodtbtt,orotL cJLAuae|
domf, no7vun,enu,aaF, u ceTb
ecJLucuulecrsArcT ceTb ("u)r=" eLeJweHToB
npul r,ro6aw E = E .
(rE
,
y
,O,n
a
n o ro p d r
(yr)r = = , ir olat t 4a a ,c fln,
V )eT
2.6. fl,na nto1oeo ellArperuHe?ocooreercrrufl, T eatno,ml'eH,o
f,Y(f)- vs (I)c ns (f).
vv(f)c
IIpu erolt, gg(f),
Vf, (t)-aro
a & M t t H A r b t ea, V V ( f )
u s\'(I) -
cooreer-
cT 6eH,HO OTnpbLTbLe il,HOilCeCTBA.
( llcnoubre B,RJIroqeHu.fl
6econopnrr. TaHran o6paaolr, c yqeroM coo6paxesufi gnoficrneuuocrlr ycraHoBrrM AJrfl orrpeAeJrerrHocrr4
BaMnrryrocTb Y gtrpeneJra.
Ecru V - erasAaprrrafl ornpbrrarr oxpecrHocrb ro.rxr !J' trs cl VE (I),
ro uM eer c f f A = V fl (I), g n n K o ro p o ro A e V. [xn re W (g) ro[brqeM A "
ran, uro6rr 6rrno A" =p(r(A))
n (*, A")=f.
. f l c n o , - q t r oA " = V , t t 6 o V orpecrnocrb A. trIran,
or
( Yr = p ( g ) ) ( v V e
(A')) (EA" e V)
( * , A" ) = l .
lIcnonray.fitrpIIEqIITIIIAeaJIvBa\vI\BbIBoAIIM:a,='Yg(f).>
2. 7. I ly c r a X, Y -ro n o rl o ? u a e c v ,u e n p ocrp& H ,crl a)IcX X Y .
7neueaJLeItrtdbt,y r eeprc) eHua,:
(1) | - ornpb\roe cooTsercreue (: corpaHf,eT oTnpb|Tbleil,trduffecrea\;
(2) T ornpatro 6 na,uc7ofiroq,ne (n, y) e l;
O r o n o , n o e u v e c n l r r n o r r , f , . T t l f , r6, n u a n u a n H e n p e p b t l H o c r t l
153.
( 3 ) e c , n t lU c* U , r o l - ' @ ) c l i m i n f s = = f- 1 ( y u );
( 4) ec r lu Ue+ A, ro I-' (y ) c l i m s u p g s s l - ' (yu)
(2) -- (3). flpem4e Bcero BaMerrrM, qro ycJroBlre orxpbrrocrr4 B crano 3 u a q a e r c rre A yl oqee: (V A ' x A ) (l r' = * \
4 a p rnof t r or r ne ( * , A)= T
(r', U') e I. Snaqur, rpu r eT-'(A)
lr rrro6ou E - +*
AJrrr Her(oroporo
s ' x z B b r [ o J r r r e H(or ' , A ) e f ,
r. e. fieliminfc="I-t(y,).
( 3) * ( 4) . O ue B rrAH o .
(4)* (1). Ecnra I ue ornpbrro, ro rrMeercfl or,KpbrroeU B X, AJrfl Koroporo f\f (U) He aaMrHyro. I4r.ar, cyilIecrRyer cerb (A)= y\f (U) ra11a.n,
naft4ercn (cp. 23) cerb (".)u=",
ero /s * A a A e|(U).
finnBcflHororeU
cxoA.Errlaflcfl,r( t u ,o6naAaloulaflteu 'cnoficrBoM,rITo #6 e I-r (ye). -fl'cuo, rrro
AJIfl E = *oo 6yget freeU. flonyuaerc.fl rlporunopeune. F
npocrpz,trcrra u T eX)(Y.
?neuea2.8. Ilycro X, Y - ron\rlo?urdecw,ue
y
perc1
e
ldu.r,
tdbl r ee
:
JLerdr
,
( 1) T - aau, n H ,Arorw
e n u re c re o e XX Y;
( 2) ec r lu Ue+ U , ro l i m s u p 6 = " I-t (y .) - I-' (y) ;
(3) ecrltl Ue* U, ro lim infg=eI-t (ye) - I-t (y) .
neJle, to uafi.qyrc.E rrHAeKc E = ** Ir aJIeMeETfr' x r1 Aqrfl-Koropbrx (t', Ae)e
e I. flocr(oilbxy AeF U,,Mbr Br{ArrM,qro (*, U) e |
(n6o n I nxognr 6ecHoEequo flnuaxufr, n aroft Toqne aneueur)
(2) * ( 3) . O ue ru s n o .
(3)*(t). Ecna (rE,U)eI
u r E * f i , A t * A , r o c yqeroM reopeurr 1.9
6y4erreliminfe==I-l(v).Crarro6rrrr,(r,a)=T.>
2.9. IlpeAJrox(errus.2.7 u 2.8 Sanruuecntr BocxoAflr n }typarononouy [8],
cM. ranlne reopeMw 1.2 u 6.2 B [3].
S 3. Konrnanrnocrb u ey6nenpepbrBHoerb
3.0. B arou uaparpa(fe Aarorcfl craH4apruble u EecrauAaprHbre Hprrreputr. r(oMrranTrrocrrr r4 aHaJIorarIHbIx troHsrnfr. 4nn (punbTpoB, gera.uubnpyron{Ee Kracctrqecfirre Sanrrr HecraHAapruoft o6qeft rotrorrornr [5, 6]. flpune4eubr rrpnJroxterrrrfl K Teopru cy,6nenpepbr'BubrxcoorBercrnufi, paaaurofi n [3, 4].
3.1. (Dunrrp g (n rorloJrorllrlec'KoMrrpocrpaucrBe X\ rraabrBaror noJwn&nrtrbtn, (cn. [Z]), ecJra namgrrft {unrrpl
6onee donxuft, .ter F, urueer
Toqr(y rrpunocuoBeutr.ffB X. CoornercrBerrHo cerb HaabrBalor nonnanrruofi,,
ecJrv.fialfiAa.fl ee rroAceTb uMeeT cxoAflrqyrocfl rroAcerb.
3.2. Cran7aprnutti fiuanrp I e X ae.naerca, noil,nanrH,blJtr6 ToM u ro.nbK,o'Tolrr,cJrAvae,ecJru nagc1aa rovna e?o J)toru,a1at,
ono.nocran0apru,a: p(9\=
c nst (X) .
{ -+ flycrr
x e V@) . Paccuorpuu ynrrpaSr,rfibrp (r),: *{(l c X:
teU|
B rrcxoArroMrrpocrpaHcrBeX. flcno, uro (*)=9
a, craJro 6rrrr, rrMeerc.fl cTalrAaprHafl Toqnare' tana.fi, qro fr x fr' . Tlumur cJroBaMr4,
# - omonocTaHAapTHaflTorrfia.
* Ecnr I = 9, ro p\9)c p(g). flycrr r e p,(9). Tor4a r e nst(X),
T. e. gJrff rrenoropoft r' e'X
6y4er r x rl . flocnegnee oaHaqaer, qto a' ?oqna upuxocHol,ewufr.F.
3.3. Qy.norp I e X ae,naerca noJwn&nrvblJtt,
6 ToJtctr rorlbtto row cJLauae,
ecJLu O"na ,nrc6oeo ornpblTo?o nonpbtrufl, Jw,tdoilcecrlaX ttafi,7erca nordeHLlne
no1nonpbtrue' H,enoropoeoeJLeMeH,Ta
ua g.
HoMtranrerr, ro W@)cnst(X).
Vvrarrrnan, qro nst(X) Jre?ntrr B MoHatre
nro6oro crarlAaprHoro tronpbrrrr.fiE, nrtnogav: (tr/e 9) (vr= F) (flE e'6'S
fi e E. B KasecrBe l4cnoMoro .F Morr(HoBg.srb nro6oft '6ecnoneqHoMaJrbrftaneMOHT 9. fIpnMeufl.fi rlocJleAoBareJrbrrotrprrHqr{[br rdAeaJrrraaqurrr4 rrepeuooa,
uoilyquM rpe6yeuoe.
r54
C. C. Ityrare.na?se
* Ilycm 6 - ornpbrroe rror(pblrlle X u p(E) - o6re4znerrlre crauAaprHbrx aJreMerrreB6, r. e. MoHaAa6. flo npnnqu,ny [epeuoca rrMerorcfl crau[apruoe F eg,r4 roEeqHoe cranAapruoe troAMuo]necrBoEo B 6 rattuq qro
Suaunr, p(g)-W(6).
b r, o n s t ( X ) UEo=F=p(g).
O c r a e r c nB c r r o M r r r r rq
aro B Toquocrrr [epeceseHrre Morre/{,crauAaprubrx ornpbrrbrx fronpbrtufr X, V
3.4. CSopruyruporannrrft B 3.3 rptrBHaH Aerraer ecrecrtseuHbrMrroucn
anaJrora Kprrrepr4.trXayc4op,Sa 4nn {ra_nrrpos. B aroft cBfl'Bur6y4en paccMarprdBarbpaBnoMepuoetrpocrpancrBo (X, %).
3.5. @ran}rp I
n X uaebrBaror 6noltH,eo?parduueH,Hblwl
ecrr4 AJrfl Kaffigoro onpyrfieHr4fl U e0L[ rrMeercfl Houerrrrafl (J-ceru Henorqporo aJrer{esra F
$wwpa 9.
3.6. @znrrp I
e X naarrsaror norLrdblwlecilu nam4rrft {nnrrp }torur,
6onee ronnraft, uewrF, cxo4rarcx n X.
3.7. Cran1apru,auil, fiu"oorp fl,BJlfl,ercfl,noJLttbLMI Tort,r,u roJLblto rorw
cJLAH&e) ecrlu nattc)aa npe}cran1aprnaa
roqft,a eao ltolta7at, onoJLocran)aprna.
{ -> flycrr g - norunfi Sramrp v. fre pst(X) n W(g\ - upeAcrauAaprHa.fl Torrxa MoHaAbr9. \peacTaHAaprHocTb / oaHarraer,qro / Jrex(rrr B MoHa}torura 9. flpn eroM V(F\n W@)+ g. flcno, qro
i1e rrenoroporo $unrrpa
BepxHflfl rpaub I n I - aro $nnrrp ltonrn r4, craJro 6rrrr, rrMeercfl Torrr(a
.r'eoX,
v, r=nst(X).
O r c r o g ar ' 4 r
A J r f ln o r o p o f ir, ' = W ( 9 ) n W ( g ) .
+- flycrr 9=9
vg-{nnrrp
}topr. Ecnn reW(9),ro
reV(F)=
cnst(X).3rraquT'y9ecrsToqKa[puHocHoBeHIIfl.>
3.8. Cran,}aprnutti $tt,nurp nerlnercfl, Bnorure o?paHulteH,rdblw
6 ToJw u
Totblto roilt cJLAHa,e,
ec"'ttLnauc}aa roqna e?o rLoHa}at npe}crau,6apru,a.
{ -> flo nprauq?rrry[epeHoca AJIfl Ha]r(AorocraHAaprHoro onpy]r(euws.U
uJ 0l,l raMerorcflcTaHAaprnrrr,laner{euT F Srrnrrpa g rr KoHetrrHoe
cranAaprEoe MHotnecrBo,E taxue, .lro f/ (E)= F. Crano 6nmr, Wg)c. U (E). Telr caI r r br r rA r r f l.t = W (g )
n n ro 6 o ro [J e " o l tr 6y4er r= [J(r' )
trpr{ rroA xoA fl qeM
crarrAaprHoM r' . flonornnnr I :: x{[/ (r'): (J = 0lI, r = tl (r')\. flcuo, rrro
9 - 6aawc {ra.nrtpa ltoruu lr r = W(9) lro rocrpoeHr4ro. CnegonareJrbrro,
$(g) c pst(X) .
<- ,{onycruru, qro pacoMarpraeaeMnrit
Snntrp g ranoB, rrro W(F)c pst (X), , rerM He Meuee F ue B,rroJrHe
orpaHl{qen. flo il,pr{Hqrrrryirepeuoca
Ilr{eercfl cTaHAaprrroeonpy}fieHrre U v.s "Q.,1tattoe, rrro AJrflBcflKwx F e"9
tt
nro6oro craHAaprnoro KoHeqnoro MHo)r(ecrBaE uaft4ercfl. r e F, rie ilofraAaroulnii B U (E). flo rprruqlrrly lrAeaJrrraaqrrr4r4Meercfl Drr,eMeurr e p(9)'
raHoft, qro r # tl (A) Arrfl HaffiAoro craHAaprHoro A = X. IIo, ycnonuro r e.
e p(9 ), rAe I - $znrrp }tomr,r.Boerlrelr G e'9 rax, uro6rr 6nrno GX G c
c'U. Tor4a [;-rfl BC.HKoro
Borrper(rrr{cxoAa e G nnruorrHeHor'e V(9)-U(v)
Eorry .AorryqeHr4ro.
3.9. Kplrreprafi Xayc4op{a gu Surnrpon.
@utarp fr,rrrfl,ercfl,r+ownar(,rHbllt
8 TOM U TO,nbHO TOM CJLAUA?I eC&U,-Oru'nOrLOt{,U SnOJLIde OAqAHUUeTL.
{ -> flocrarouuo pa6orarb B crarrAaprHoM auTypaffie. Ecnn I xolrnarrerr, ro IL(g)cnst(X)
no 3.2. V'.rurnrsa.fl,qro nst(X)cpst(X),
aanilroqaeM:
I no;l.on rr BrroJrneorpanrrqeu.
.- Ecnz F anonue orpauzqeu, ro uo 3.8 p(g)cpst(X).
Ectn I
nor I oE , r o lr ( g ) | l p s t(X)= n s t(X ). O rc ro ga B brB oA rrM:
p(g):
pst(X
)0
W (g)
c ns!({). Ocraercs cocJrarrc.Ena 3.2.
3.10. Hafi4enubre rlptrBrrafir4 Moryr 6rmr rroJro)fieubrB ocuoBy r4ayqenv.fl.
paailI4qublx TorloJlorrrueorrrx uon.aruft, 6nuaxlrx H HerrpepbrBrrocrrr. OcranoBrrMcfl BAecr,Ha oArroMnB Hr4x (cv'. [2-a]\.
3.11. CoornercrBlre f, geficrnyroqee ue X n Y, uaebrBaror cy6nenpepu,sItbtJtt e roqn,e fr. vB dom l, ecJrrr o6paa Srnrrpa e.Kpecruocreft roqxn r npw I
flBirflerc.fl noMrraHTHbIMB Y. Coo'rnercrBze l, cy6neupepbr,BHoeB nam4oft
Toqne dom l, HaabrBarorcy6nenpepblrtrblJn.
3.12. CranlaprH,oe cooreercrrue T ua X e Y cy6nenpepblsno I row u
ro.nbnororw c.nAq,ael
ec.nu I (nst (X) )c nst (I).
O r o no,noeuve cnu t no rr,fl,Tnn t, 6.0uanux n He np ep bt,e H,oeru
t55
'
{ flonaaareJrbcrBocJleAyer r{B 7.2 n 3.2, v6o nst(X) rpeAcraBJrfler co6ofio6reF[EeEIIeMoIIaAToqgRcTaIIAapTHofofl[pa.X.>
3.13. Cooreercrlue cyfu,enpepbteno 6 ToM u roJlbno roJtt,cJLAHaelecJLu
oH,onepeeoilur rcoil,nanrnw,e fiu.nbrpbl 6 ttownaw,Ttrbte.
{ IIocnoJID,-r(ySrnrrp oxpecruocreft Toqxz BaBeAoMonoMrrar(Terr,AocraToquocTbtrptrBe4eunoro ycJIoBItfl 6eccmopna. flyctr Terrepb Bapanee rraBecrrro,
ttTo coorBercrBrre cy6neupepbrBrro. Eea ywraneur,rsodqnocrrr Molr(Ho pa6orarr
ts crauAaprrroM aurypaffie. flpznnexarr 3.1,2 u. 3.2, nmpvM, rrro n gannoft crryaqtrtr o6paa crarrAaprrroro noMtraxruoro {uumpa
KoMtranTe.rr.Ocraercs
cocJrarbcfl Ha trptrEqra,truepenoca. D
3.14. B cssau c fiplrrepueu 3.13 cy6ue,npepbrBubrecoorBercrtBtrfi.EaBbraaror rruorAa Horv,nanrrrbltw,u
(cp. [2]).
3.15. Cy6nenpepbtsn.oecoor6erci:r6ue,)efr,creyrou4ee6 rayc\op$oso npocTp aH,cT6o, cor p aH,fl,e
T oTH,ocuTeJLbIIarc noMn&nTH,ocTb.
ro U_ c_ns t ( X ) . Cr aro 6 u rr, I(U )c n s t(Y).
Iz l anecrno[5], uro B aroM cl ryvae | ([/) ornocareJrbrro KoMtraxrHo.
3.16. IIycro T - aaunlraroe cy6nenpepblrru,oecoorlercreue.' Toe\a I
nolLyH,enpe
pblsno c6epfra.
{ flo trpruqrrtry uepeuoca Mornno pa6orarb B craEgaprnoM arrrypame. .
. ?Irar, uyorb A - cranAaprHoe saMnrryroe Muolr(ecr,Borr r e cll-t (A). Tlrrtea ' e ' A 6y4er (fr' , a' )ef.
P as.a' e
e rn ci ifr' N f i, A J r f 'i.Horb p o ro trp rH e r(o ro p o M
€ I (nst (X) ), to naftAercfl craHAaprnoe a n o6paae, Atrrfl r(oroporo a x a' .
&eA. B cr,rJryBaMnuyrocrn I BbrrroJrueno
B cury BaMnHyroww A BbrBoArxM:
(r, o)ef. lfuar\ n= f-'(,4).
Z.tl. flpegromeurre 3.16 $aHtmueoHr ylcranoBJrenoB 147 o6o6rqaet
"c noMoqbro
6onee pau.HgeyrBeplltAenrre o SynHqvrflx vB [3]. B Bar$rroqeHfre
TeopeMbr {..9 gaAuM rrpocroe rrecraH,4aprHoe;(onaaareJrbcrBose6olruroft uo4u{ranar1trn Hptrreprrr HerrpepbrBnocrvr5.1. ua [3].
3.18. Ilycra f: X -. Y - $ynrcr4ua, leficrayrcu4an 6 rayc1op$oeo epocrpaH,crso. Toela I u,enpepblrHa B ToM n roJlbno rolw c,nAu&e1ecr,u 1na, naenOofi rovrcu fr na X uneercfl, eJLewerdr
A ua Y ranoti, t4ToAcJlorue frE-+r 6JLever c7urlecrsolarrueno7ceru ("n)n=*, 0ta noropofr,f (rr)* A.
{ Hyat4aercfl B trpoBepr(e Jruurb Aocraroqrrocrb cSopuynrrpoBaEuoro
trpr,ranana. Ey4eu pa6oraru n crarrAaprnoM arrrypame. IIo ycJroBrrrouMeeM
(Yre-*.n) (syn -* A)
(rr, a)=f.
Ha ocgotsauurr reopeMbr I..9 trocJleAHeecoorrrortreHr4e Mo}r(Eo trepetr[carb
B BITAE
:
(Y*' o r) (sA' N A)
B qacrsocrrr, AJI.EEemoroporoU'xA
Y B a x J l r o q a e fqt rr,o A : f ( r ) .
" q o p S o- n o c r w
(pynnqna. tr
IrerrpepbrBna.fl
r. e. I
(i', A')= f .
B c4ry xaycrrrmollHerroy'-t@).
ItpoMe roro, fi'xr"*f(fi')*l@),
JINTEPATYPA
:
'7;Dotecki Sz. Tangencyand differentiation: some applicationsof convergencetheory.Alnali tli Matematicapura ed applicata,1982,v. 13Qil n3-255.
2. Penot .7.-P.Compactnets, filters and relations.- J. Math. Anal. AppI., {9E3, v. 93,
N 2, p. 4m_,4fi.
3. Faller R. V; Relations among continuousantl various .non-continuousfunctions.Pacific f. Math., 1968,v. 25, N 3, p. 495-509.
4. Smithson R. E. Subcontinuity for multifunctions.- Pacific I. Math., 1975,v. 6{, N 4
p. 283-288.
t56
5. Lusemburg W. A. J. A general theory of monads.- In: Applications of model theory
to algebra, ana.Iysisand probabilify. New.York: Holt, Rinehart aud, Winston, 1969,
p. 18-86.
6. Stroyan K. D., Laxembur1 W. .A. I.Introtluction to the theory of infinitesimals.New,York: Acad. Press,1976.
7. Aarnes ,. F.t Anilenaes P. n. Oa nets anil filters.- Math. Scan(L, 1972,.v. 3|', N 2"
p. ?85-292
I
9, frgrare&a|ae C. C. llu(prunreBtrMaJlbubreaacareJlbnbrerouycbr.- (ou6, uar.' *rnt.,
1985,r.26, N 6, c. 67-76.
e. Eoeocu6upcn
Craran.nocrVnulLa
24 aneapa 1.985 e.
I
tf
)