Huinga kiato

huinga kiato ko te wāhi topological tautuhi i roto i te taupoki i te subcover tahuti. wāhi kiato i roto i te āhuawhatunga o ratou āhuatanga e rite i te pūnaha o huinga tahuti i roto i te ariā hāngai.

huinga kiato ranei CD - he huinga o te wāhi topological, piri nei i te momo o te wāhi whāiti.

Āhua kiato (precompact) Kei te whakaturia anake i roto i te take o te taiawhio whāiti. A, no te tohatoha wāhi i roto i te subsequence convergent kia huaina ai reira raupapa kiato.

huinga kiato He āhuatanga motuhake:

- he tikanga kiato tetahi whakaatu tonu;

- huinga kati tonu kua he kiato;

- bijection tonu, tautuhia nei i runga i te kiato pā ki homeomorphism.

Tauira huinga kiato he:

- iti a katia huinga RN;

- tautuhiroto tahuti i roto i ngā wāhi e ōrite te axiom o wehe m T1;

- Ariā Ascoli Arzela characterizing huinga kiato mō etahi wāhi mahi;

- wāhi Stone no ki te taurangi Boolean;

- compactification o te wāhi topological.

Whakaaro i te tūranga i whakaritea te ao ki te pāngarau, ka taea e tetahi tautohe e ko te huinga e Kei roto he plurality o ngā āhuatanga ki te āhuatanga motuhake tenei. Āpiti atu ki ngā tetahi huinga hypothetical kōrero ngā wāhanga vai ariā. Heoi, e tika ke ki te ngako rawa o te huinga ona āhuatanga.

I roto i te mara o te huinga ao tauhanga timatanga kanohi e te huinga o tau tōpū. Heoi, he wāhi motuhake no ki tenei huinga i roto i te huinga ariā.

Ko te huinga o tau tōpū ngā te huinga o huānga (tau) e kia whakatika fakanatula i roto i te tatau. E rua ngā ara i roto i te whakatau i te tau māori:

- whakawhiti o ngā tūemi (tuatahi, tuarua, me ētahi atu);

- te maha o ngā kaupapa (kotahi, e rua, me ētahi atu).

I roto i tenei take, e kore e ngā-tau tōpu kore me tau tōpu tōraro ki te momo māori o tau tono. I roto i te mara pāngarau o te huinga o ngā tau māori ko N. he mutunga tenei ariā, te whakawhetai ki te aroaro o tetahi maha o te tahi atu momo o te tau tūturu tūturu nui atu i te tuatahi.

Rerekē taiao, kua whiwhi tau katoa i te whakatinanatanga o ngā mahi pāngarau i runga i te tau māori rite tua tangohanga ranei. whakaritea te huinga o tau tōpū i roto i te pāngarau te Z. Na tango nga hua o tua atu me te whakarea o tau e rua ko te maha o te momo anake o te momo kotahi. Ko te hiahia hoki tenei momo o tau takanga tika ki te kore o te kaha ki te whakatau i te rerekētanga i waenganui i rua tau tōpu. Ko reira whakaurua Michael Stifel ki te pāngarau tau tōraro.

titau te reira i whakaaro tupato ki taua ariā rite wāhi kiato. whakaurua tēnei wā ko PS Alexandrov ki whakaū te whakaurua te ariā o te wāhi whāiti ki te pāngarau o Frechet. Ko te māramatanga ki tonu i te momo topological wāhi kiato i roto i te take o te subcovering fakataimí ia hipoki tuwhera. I roto i te whanaketanga o pāngarau muri, ka te compactness wā he tikanga o te nui ki runga ake i tona tauira raro. Na inaianei kua matau ai e te compactness compactness, a ko te tikanga tawhito o te wā i roto i te taitara o "countably whāiti." Heoi, he ōrite ngā ariā e rua ka whakamahia i roto i ngā wāhi ngahuru.