Isethi compact

isethi Compact isikhala topological kuchaziwe ikhava okuyinto subcover ezilinganiselwe. izikhala Compact ku yomphindwa izakhiwo zabo zingase zifane simiso amasethi ezilinganiselwe imfundiso okuhambisanayo.

isethi Compact noma i-CD - isethi engezansi isikhala topological, okuyinto esibangelwa uhlobo isikhala ezihlangene.

Ngokulinganiswa compact (precompact) isethwe kuphela uma isifunda ezihlangene. Ngesikhathi kunikezelwa isikhala endaweni subsequence convergent kungase ngokuthi ngokulandelana ezihlangene.

isethi Compact anezakhi ethize:

- ngendlela compact iyiphi isibonisi okuqhubekayo;

- isethi engezansi avaliwe has njalo icwecwe;

- bijection okuqhubekayo, okuyinto kuchazwa ku-compact libhekisela homeomorphism.

Izibonelo isethi compact yilezi:

- kungagcini avaliwe amasethi RN;

- subsets ezilinganiselwe ezikhaleni ehambelana Axiom ka divisibility T1;

- Theorem Ascoli Arzela esibonisa isethi compact izikhala ethile wesitayela;

- Stone isikhala okuqondene algebra Izimiso eziphusile;

- compactification isikhala topological.

Uma ucabangela jikelele isethi isikhundla wezibalo, umuntu angabona baye bame kwelokuthi lokhu kuyinto iqoqo okuyindawo ehlanganisa sebuningini izakhi izakhiwo ezithile. Kanye elinye iqoqo yezinto kuhlanganisa izingxenye ezihlukahlukene okuxoxwa umqondo ukhona. Nokho, impahla yayo eziphambene uqobo isethi.

Emkhakheni wezingalo aphansi izibalo isethi jikelele imelelwa iqoqo integers. Nokho, indima ekhethekile kungokwalabo le isethi e isethi theory.

Isethi integers kuhlanganisa iqoqo izakhi (izinombolo) ezingavela ngokwemvelo ngesikhathi kubalwa. Kunezinhlobonhlobo zezindlela ezimbili ekunqumeni izinombolo yemvelo:

- ukudluliselwa izinto (kokuthoma, kwesibili, njll);

- Isibalo izifundo (kunye, kubili, njll).

Kulokhu, ezihlukahlukene ezingewona integers futhi integers engakhi uhlobo engokwemvelo izinombolo azisebenzi. Emkhakheni nezibalo isethi izinombolo yemvelo N. Lo mqondo engapheli, sibonga khona iyiphi inombolo yezinye izinhlobo inombolo yemvelo zemvelo esikhulu kunesokuqala.

Ngokungafani zemvelo, tinombolo letiphelele etholakala ngokuzikhandla ukuqaliswa imisebenzi zezibalo ku izinombolo zemvelo njengoba kwalokho noma nokukhipha. Isethi integers mathematics lumiswa Z. ngu nekususa imiphumela kwalokho kanye ukubuyabuyelela wezinombolo ezimbili inombolo uhlobo kuphela yohlobo olufanayo. Isidingo salokhu uhlobo nesenzakalo izinombolo ngenxa yokuntuleka Ukukwazi ukunquma umehluko phakathi integers ezimbili. Kuyinto Michael Stifel wethulwa Mathematics izinombolo engemihle.

Kudinga sokucabangisisa imiqondo ezifana isikhala ezihlangene. Leli gama yethulwa PS Alexandrov ukuqinisa umqondo isikhala compact is busuka wezibalo of Frechet. Siyiqonde ngokugcwele uhlobo topological isikhala compact uma subcovering ezilinganiselwe isigubungelo ngamunye evulekile. Ngo ukuthuthukiswa okwalandela wezibalo, le compactness elithi baba umyalelo ezidlula ephakeme kunaleyo sabafowabo aphansi. Nyalo kuqondwe compactness compactness, futhi umqondo endala gama esihlokweni "countably ezihlangene." Nokho, kokubili imiqondo yamagama okulingana uma lisetshenziswe izikhala imethrikhi.