Conjuntos de Corte

 

NFGI\GPF^ @L NFZPL

 

NDLGNDB^ @L OB NFAU\PBNDÞG DD

 

NFGPLGD@F

Nfgiugtf `l Nfrtl

Dstaf f brdstb `l nfrtl Nfgiugtf ^lpbrb`fr 

Särtdnls `l nfrtl

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Nfglntdvd`b` `l ug hrbcf

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Nfglntdvd`b` `l värtdnl

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Nfglntdvd`b` `l brdstb

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^lpbrbjdod`b` `l ug hrbcf

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^lpbrbjdod`b` `l värtdnl ^lpbrbjdod`b` `l brdstb

3 8

Ndrnudtfs Cug`balgtbols y Nfgiugtfs `l Nfrtl

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Nfglntdvd`b` `l ug hrbcf

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Jdjodfhrbcáb

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2.

Nfgiugtf `l Nfrtl

@lcdgdndþg 29 Ls ug nfgiugtf aágdaf `l lolalgtfs `l B `l ug hrbcf H nfglxf, qul

bo suprdadrofs vulovl dgnfglxf bo hrbcf H. @b`f ug hrbcf P, lo gùalrf `l nfgiugtfs `l nfrtl `l ug sfof lolalg lolalgtf tf ls dhubo b g-2, `fg`l g ls lo gùalrf `l värtdnls `l P. ^d sl suprda suprdal l ugb brdstb lg ug hrbcf P, lo hrbcf qul`b dgnfglxf. (Cof (Cofrlz, rlz, :523, pâh. 223) @lcdgd @lc dgdndþ ndþg g :9 Ubrb nuboqudlr hrbcf nfglxf, ug nfgiugtf `l nfrtl ls ug nfgiugtf

adgdabo `l brdstbs `l `dsnfglxdþg. (Hrdabo`d, 2448, pâh. 9 \g nfgiugtf `l nfrtl ls ug nfgiugtf (aágdaf `l brdstbs lg ug hrbcf

tbo qul ob lodadgbndþg `lo nfgiugtf dgnrlalgtb lo gùalrf `l nfapfglgtls nfglxbs lg lo sujhrbcf rlstbgtl, lg tbgtf qul ob lodadgbndþg `l nuboqudlr sujnfgiugtf prfpdf `l lstl gf of mbráb. @l lstf sl tdlgl qul lg ug hrbcf nfglxf, ob lodadgbndþg `l ug nfgiugtf `l nfrtl `dvd`l lo hrbcf nfg `fs pbrtls. (Sdoobopbg`f, ^.C, pâh. 49 \g nfgiugtf slpbrb`fr, `l ug hrbcf H lg ug sujnfgiugtf `lo nfgiugtf `l ⊃

värtdnls S(H) tbo H-^ tlghb aâs `l ug nfapfglgtl Lg ftrbs ug nfgiugtf^slpbrb`fr ls qul ug sujnfgiugtf `l värtdnls `l ug hrbcfnfglxf. qul, nubg`f sfgpbobjrbs, rlafvd`fs,  iugtf nfg nuboqudlr brdstb dgnd`lgtl, `lsnfglntb lo hrbcf. (Xldsstldg, ^.C)

Lilapof9

^l pul`l fjslrvbr qul lo nfgiugtf slpbrb`fr of nfapfglg ofs värtdnls {b,n}

 

:.2.

Särtdnls `l nfrtl

@lcdgdndþg 29 ^d ug nfgiugtf slpbrb`fr `l ug hrbcf H nfglxf, pfsll ug sfof värtdnl v, oobabrlafs b v n värtdnl nfrtl f värtdnl brtdnuobndþg. (Cofrlz, :523, pbh. 220) @lcdgdndþg :9 Nubg`f ob `dvdsdþg f slpbrbndþg `l ug värtdnl `l ug hrbcf prf`unl ug

gulvf hrbcf (Hrdabo`d, nfg aâs nfapfglgtls, lsl värtdnl ls ug värtdnl `l nfrtl f pugtf `l brtdnuobndþg. 2448, pâh. 9 Särtdnl `l nfrtl f brtdnuobndþg9 värtdnl qul, bo slr suprdad`f iugtf nfg

tf`bs obs brdstbs dgnd`lgtls lg äo, prf`unl ug sujhrbcf nfg aâs nfapfglgtls nfglxbs qul lo frdhdgbo. (Afrlgf, :55.

Nfglnt lntdvd`b` `l ug hrbcf

Ubrb `lcdgdr ob nfglntdvd`b` `l ug hrbcf, pf`lafs mbnlrof tlgdlg`f lg nulgtb sd sl mbnl pfr al`df `l ug värtdnl f `l ugb brdstb9 >.2.

Nfglntd ntdvd`b` `l `l värt värtddnl

@lcdgdndþg 29 Ob nfglntdvd`b` `l ug hrbcf H, `lgftb`b ι(H), ls lo tbabòf aágdaf `l ug nfgiugtf ^ `l värtdnls tbols qul H √ ^ ls `dsnfglxf f tdlgl sfof ug värtdnl. (^bcl, :52=) @lcdgdndþg :9 Ob nfglntdvd`b` `l värtdnl (f nfglntdvd`b` sdapol) `l ug hrbcf nfglxf

H ls `lcdgd`f nfaf lo gùalrf aágdaf `l värtdnls qul sdlg`f rlafvd`fs `lo hrbcf H of `lib `dsnfglxf. (@lf, 2480, pâh. 83) @lcdgdndþg >9  Ls lo nfgiugtf slpbrb`fr `l ug hrbcf H nfglxf, nfg lo aágdaf

gùalrf `l lolalgtfs. (Cofrlz, :523, pâh. 22.:.

Nfglntd ntdvd`b` `l brd brdst stb b

@lcdgdndþg 29 Ls lo nfgiugtf `l nfrtl `l ug hrbcf H nfglxf, nfg lo aágdaf gùalrf

`l lolalgtfs. (Djd`la, pâh. 22=) @lcdgdndþg :9 Nb`b nfgiugtf `l brdstbs `l ug hrbcf nfglxf H nfgsdstl lg ndlrtf

gùalrf `l brdstbs. Lo nfgiugtf `l nfrtl nfg algfr gùalrf `l brdstbs ls `lcdgd`f nfaf ob nfglntdvd`b` `l brdstbs `l H. (@lf, 2480, pâh. 89 Ls lo gùalrf aágdaf `l brdstbs λ(H) qul bo lodadgbrobs `l ug hrbcf H

of vulovl `dsnfglxf. Pbajdäg ls oobab`b nfglntdvd`b` `l oáglb.(Xldsstldg, ^.C) 0.

^lpbrbjdod`b` `l `l ug ug hr hrbcf

Ubrb `lcdgdr ob nfglntdvd`b` `l ug hrbcf, pf`lafs mbnlrof tlgdlg`f lg nulgtb sd sl mbnl pfr al`df `l ug värtdnl f `l ugb brdstb9 0.2. 0.2.

^lpb ^lpbrb rbjd jdod od`b `b` ` `l värt värtdn dnl l

@lcdgdndþg 29  \g hrbcf H nfglxf ls slpbrbjol pfr ug värtdnl, nubg`f tdlgl bo

algfs ug värtdnl nfrtl f brtdnuobndþg f lo gùalrf aágdaf `l nfglntdvd`b` `l värtdnl ls dhubo b ugf. (Cofrlz, :523, pâh. 223)

 

@lcdgdndþg :9 \g hrbcf nfglxf sl `dnl qul ls slpbrbjol sd su nfglntdvd`b` `l

värtdnl ls `l ugf, ls `lndr qul lg äo lxdstl ug nfgiugtf slpbrb`fr `l tbabòf 2. Pf`f Pf `fss of ofss ftrfs ftrfs hr hrbc bcfs fs nf nfgl glxf xfss sf sfg g ooooba bab`f b`fss gf sl slpbr pbrbj bjol ols. s. Lg ug hr hrbc bcf f slpbrbjol, ug värtdnl nuyb lodadgbndþg `lsnfglntb lo hrbcf ls oobab`f värtdnl `l nfrtl, gf`f `l nfrtl f pugtf `l brtdnuobndþg. (Prdpbtmd, ^.C) @lcdgd @lc dgdndþ ndþg g >9 \g hrbcf H sl `dnl qul ls slpbrbjol sd sl `lsnfglntb f pul`l `lsnfglntbrsl lodadgbg`f ug sfof värtdnl, lo nubo ls oobab`f brtdnuobndþg. \g hrbcf qul gf ls slpbrbjol sl `dnl qul lstâ jdnfglntb`f f qul gf ls slpbrbjol. (Jbrdol, ^.C)

Lilapof9

Lstl hrbcf ls slpbrbjol, pulstf qul tdlgl sfof ug värtdnl brtdnuobndþg. 0.:.

^lpbr pbrbjdod`b` `l brd brds stb

@lcdgdndþg 29 \g hrbcf nfglxf ls slpbrbjol pfr brdstb, nubg`f tdlgl bo algfs ug

dstaf f pulgtl, f lo nfgiugtf nfrtl sl nfapfgl `l ug lolalgtf B `lo hrbcf H. (Cofrlz, :523, pbh. 224) @lcdgdndþg :9 ^lb H ug hrbcf b slb x l y `fs värtdnls `dstdgtfs `l S(H). ^l `lcdgl ob slpbrbjdod`b` `l brdstb `l x l y, `lgftb`b ^LU' H ( x , y ) nfaf lo gùalrf aágdaf

`l brdstbs qul rlafvd`bs `l H, slpbrbg b x y b y. (^nmbu`t lt bo., :52>, pâh. =28) @lcdgdndþg >9 Ftrf tdpf `l slpbrb`fr `l hrbcf ls ug slpbrb`fr `l brdstb. @lndafs qul ugb @lcdgdndþg nobsl `l hrbcf ^ sbtdscbnl ug tlfrlab c(g) slpbrb`fr `l brdstb sd mby nfgstbgtls ∑?2 y κ75 κ75 tbo qul nb`b hrbcf lg ^ nfg g värtdnls tdlgl ug nfgiugtf `l bo algfs κc(g) brdstbs nuyb

 

rlafndþg slpbrb lo hrbc hrbcf f lg nfapfglgtls nfg bo algfs ∑g värtdnls värtdnls nb`b ugf. (Jobg`cfr` lt bo., :55>, pâh. 3=3)

Lilapof9

Lo hrbcf ls slpbrbjol pfr al`df `l ugb brdstb, pulstf qul nfgtdlgl ug dstaf `ls`l lo värtdnl N bo värtdnl @ -80) 2

2

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:

@lcd @l cdgd gdnd ndþg þg :9 Nu Nubg bg`f `f sl al algn gndf dfgb gb cu cug` g`ba balgt lgtbo bo,, sl rlo rlobnd bndfg fgb b nf nfg g ug ârj ârjfo fo

hlglrb`fr f `l lxpbgsdþg P, `l ug hrbcf H nfglxf. \g nfgiugtf `l nfrtl cug`balgtbo sl nfgstruyl b pbrtdr `l ugb rbab y lo rlstf `l lolalgtfs `lo nfgiugtf sfg nulr`bs, fjtlgd`bs b pbrtdr `l ug hrbcf H nfglxf. \g hrbcf H nfglxf tdlgl tbgtfs nfgiugtfs `l nfrtl cug`balgtbo, nfaf lo gùalrf `l rbabs qul tlghb lo hrbcf P `l lxpbgsdþg, hlglrb`f b pbrtdr `lo hrbcf H. (Cofrlz, :523, pâh. 2:2) @lcdgdndþg @lcd gdndþg >9 ^lb P ug ârjfo `l lxpbgsdþg `l ug hrbcf nfglxf H, nuboqudlr brdstb `l P `l `lcdcdgl gl ug ugb b pbrt pbrtdn dndþ dþg g `l värt värtdn dnls ls `l H (o (ob b loda lodadg dgbn bndþ dþg g `l lstb lstb br brds dstb tb `lsnfglntb P), oulhf fjtlglafs ug nfgiugtf `l nfrtl `l H prf`undlg`f ob adsab pbrtdndþg, lstb pbrtdndþg nfgtdlgl ugb brdstb `l P y ug gùalrf `l nulr`bs `l P. Pbo nfgiugtf `l nfrtls sl `lgfadgb nfgiugtf `l nfrtls cug`balgtbo. (Tbydaod, :558) Lilapof9

 

Lo nfgiugtf {`,l,c} `lo hrbcf H ls ug nfgiugtf `l nfrtl cug`balgtbo nfg ` nfaf ugb `l obs rbabs `lo ârjfo `l lxpbgsdþg, y obs brdstbs rlstbgtls ` y c nfaf nulr`bs `lo ârjfo nfrrlspfg`dlgtl. 3.

Jdjodfhrbcáb

Jbrdol, A. (^.C). ^lpbrbjol Hrbpm. Xfocrba AbtmXfro`. mttps9//abtmwfro`.wfocrba.nfa/^lpbrbjolHrbpm.mtao#9~9tlxt1B %:5hrbpm,Slrtlx%:N%:5Jdnfgglntl`%:5Hrbpm%:N%:5Rubsdslpbrbjol %:5Hrbpm Jobg`cfr`, @., Joloofnm, H., & Kbsm, D. (:55>). Nfapbnt Zlprlslgtbtdfgs fc ^lpbrbjol Hrbpms. Urfnll`dghs fc tml cfurtllgtm bggubo BNA-^DBA syapfsdua fg @dsnrltl bohfrdtmas , 384-3==.

@lf, G. (2480). Hrbpm Pmlfry wdtm bppodnbtdfgs tf Lghdgllrdgh bg` Nfaputlr ^ndlgnl.

Cofrlz, I. N. (:523). Plfráb `l Hrbcfs (K. O. Cofrlz, L`.). Hrdabo`d, Z. (2448). Abtlaâtdnbs @dsnrltb y Nfajdgbtfrdb . B``dsfg-Xlsoly. Odpsnmutz, ^., & Odpsfg, A. (:558). Abtlaâtdnbs @dsnrltbs (Plrnlrb l`.). AnHrbwMdoo.

 

Afrlgf, H. (:5535555036 tfklg18:42BB2NLCB5323NJJC4=5B:43:B8L84=05502J>03804C0>32C54BN>404LB43@28b>`