Isethi compact

isethi indawo i isithuba topological kuchaziwe kwi-inshorensi leyo subcover ezisikelwe. izithuba Icwecwe kwi ithopholoji iimpawu zazo ukuze sifane inkqubo leeseti aphelayo imfundiso ahambelanayo.

iseti compact okanye CD - elucwangciso olusezantsi lwe kwindawo topological, nto leyo aqhubela yi uhlobo indawo compact.

Kakhulu compact (precompact) kulindeleke kuphela kwimeko kwisiphaluka compact. Xa kusabiwa indawo subsequence convergent kusathiwa ngokulandelelana compact.

iseti indawo has iipropati ezithile:

- ngendlela compact nayiphi uboniso okuqhubekayo;

- yenye evaliweyo usoloko compact;

- bijection eqhubekayo, echazwe kwicompact ibhekisela homeomorphism.

Imizekelo iseti compact zezi:

- limited yaye ivaliwe iiseti DB;

- subsets sokuzalwa kwiindawo ezifana saziwe of divisibility T1;

- theorem Ascoli Arzela eziphawula iseti indawo iindawo ezithile esebenza;

- space Stone besive algebra Boolean;

- compactification bendawo topological.

Ukuqwalasela isethi indawo jikelele kwimathematika, umntu athi ukuba oku isethi leyo iqulathe ezininzi izinto ngempahla ezithile. Kunye nenye iseti ezingenzeka iquka amacandelo ahlukeneyo kuxoxwa ingqiqo ikhona. Nakuba kunjalo, iimpawu zayo zichasene ngoyena ndoqo iseti.

Entsimini sabaqalayo iseti yokalo emileyo jikelele imelwe yintlaninge integers. Nangona kunjalo, indima ekhethekileyo bobabo le elibekiweyo mbono elimisiweyo.

I iseti integers iquka uluhlu lweziqalelo (amanani) ezinokuthi ephakama ngexesha nokubala. Kukho iindlela ezimbini zokwenza izigqibo amanani zendalo:

- transfer of items (okokuqala, okwesibini, njl);

- Inani lezifundo (inye, zimbini, njalo njalo).

Kulo mzekelo, ezahlukeneyo ezingezo-integers kunye integers zingathandekiyo uhlobo zendalo amanani azisebenzi. Endle zemathematika iseti yamanani yendalo N. Lo mqondo engaphele ndawo, ngenxa yobukho naliphi na inani ezinye iintlobo inani yendalo yendalo enkulu ngaphezu kweyokuqala.

Ngokungafaniyo zendalo, amanani apheleleyo afunyanwa yi ukuphunyezwa imisebenzi zezibalo kwi amanani yendalo njengoko ukudibanisa okanye nokuthabatha. Isethi of integers kwimathematika uchongwe Z. ngokuthabatha iziphumo ukudibanisa ukuphinda-manani mabini linani uhlobo kuphela zohlobo olufanayo. Imfuno olu hlobo amanani nasisihlo ngenxa yokunqongophala ukukwazi ukufumanisa umahluko phakathi integers ezimbini. UMikayeli Stifel yaziswa ootitshala beMathematika amanani akhabayo.

Kufuna ingqalelo ngenyameko ngeengongoma ezifana isithuba compact. Eli binzana kuqaliswa PS Alexandrov ukubethelela ingcamango indawo compact yaziswa imathematika ka Frechet. Ngokupheleleyo ukuqonda lohlobo topological isithuba indawo xa subcovering ezisikelwe yesigqubuthelo nganye evulekileyo. Kuphuhliso elandelayo imathematika, eli compactness elithi elaba umyalelo sezingeni eliphezulu ngaphezu nogxa awo. Ngoku ke esingaqondwayo compactness compactness, kunye ngomqondo omdala kweli binzana kwisihloko "countably compact." Noko ke, omabini la magama alingana xa esetyenziswa kwiindawo metric.