Chiine seti

Compact seti chinhu topological nzvimbo rinorondedzerwa pabutiro uri finite subcover. Compact dzezvimwe ari topology zvivako zvavo anogona kufanana kwegadziriro finite richivira runoenzanirana dzidziso.

Compact vanochengeta kana CD - munhu subset ane topological nzvimbo, iyo anonyengetedzwa kubudikidza mhando tsindirana nzvimbo.

Vashoma tsindirana (precompact) wakaiswa chete kune chitsidzo redunhu. Kana allocating nzvimbo mune convergent subsequence unganzi sequentially tsindirana.

Compact seti ane chaizvo ehupfumi:

- chitsidzo nenzira chero enderera kuratidzwa;

- up subset nguva dzose ane tsindirana;

- chinoramba bijection, iyo chinorondedzerwa pamusoro chitsidzo zvinoreva homeomorphism.

Mienzaniso tsindirana seti vari:

- zvishoma uye vakavhara anogadza Rn;

- finite subsets mu dzezvimwe kuti panguo axiom pamusoro divisibility T1;

- Theorem Ascoli Arzela zvinoratidza tsindirana yakatarwa kuti zvimwe dzezvimwe dzichipfekeka;

- Stone nzvimbo kungova Boolean nemasvomhu;

- compactification a topological nzvimbo.

Kufunga waifarirwa yakatarwa nzvimbo pamwe masvomhu, mumwe anogona nharo kuti ichi chinhu yakarongwa iyo unotora munhu muzvizhinji kuti zvinhu zvimwe zvivako. Pamwe mumwe tsvagai yakatarwa zvinosanganisira siyana zvinoriumba vakakurukura maonero ariko. Zvisinei, nzvimbo ayo zvinopesana chaizvo zvinorehwa yakatarwa.

Mumunda zvepakutanga svomhu yezvisikwa yakatarwa inomiririrwa iine integers. Zvisinei, basa rinokosha ndezvaiye yakatarwa iyi yakatarwa dzidziso.

The akagadzirwa integers unosanganisira akaita zvinhu (nhamba) angamuka tarasika panguva kuverenga. Pane Nzira mbiri Pakusarudza dzinongoitika nhamba:

- kutapurirana zvinhu (pakutanga, wechipiri, etc.);

- nhamba zvidzidzo (rimwe, vaviri, etc.).

Muchiitiko chino, siyana vasiri integers uye akaipa integers nemasikirwo mhando nhamba regai kushandisa. Mune kwemasvomhu munda yakatarwa dzinongoitika nhamba iri N. pfungwa Izvi zvisingaperi, nemhaka kuvapo chero nhamba vamwe mhando rwokuzvarwa rwokuzvarwa nhamba kupfuura kutanga.

Kusiyana dzinongoitika, wose nhamba vakawana ne Implementation pamusoro kwemasvomhu remapazi pamusoro dzinongoitika nhamba sezvo Uyezve kana kubvisa. The akagadzirwa integers mu masvomhu akasarudzwa Z. By Tikabvisa migumisiro Kuwedzera uye chokuwanziridza nhamba mbiri inhamba mufananidzo chete chete mhando. Kudiwa ichi mhando chiitiko nhamba nokuda kwokushayiwa anokwanisa kuona musiyano pakati integers maviri. Zviri Michael Stifel akatanga masvomhu asina nhamba.

Zvinoda kunyatsoongorora pfungwa dzakadai tsindirana nzvimbo. Izwi iri vakasuma PS Alexandrov kusimbisa pfungwa chitsidzo nzvimbo iri chakaunzwa samhu Frechet. The kunzwisisa zvizere topological mhando tsindirana nzvimbo pakuparwa finite subcovering nerimwe chifukidzo rakashama. In haizopereri kukura masvomhu, izwi compactness akava ndarayira unokosha kupfuura ayo yakaderera ishamwari. Zvino zvinonzwisiswa nokuda compactness compactness, uye mupfungwa yekare rokuti uri musoro "countably tsindirana." Zvisinei, zvose pfungwa dziri noenderana kana kushandiswa arşive dzezvimwe.