Olelo hoopomaikai i

Olelo hoopomaikai kau mea he topological wa ho'ākāka 'ia ma ka poi i mea finite subcover. Olelo hoopomaikai hakahaka ma ka topology o ko lākou mau waiwai e hoohalike ai i ke ano o ka finite e puhi ia i loko o ka AYEIE kumumanaʻo.

Olelo hoopomaikai kau 'ole CD - he subset o ka topological pokole, a ua poloʻai pule ma ke' ano o ka olelo hoopomaikai a puni.

KŘpa a olelo hoopomaikai (precompact) Ua waiho wale i loko o ka hihia o ka olelo hoopomaikai kaapuni. I ka hoʻokaʻawale 'makahiki i loko o ka nń subsequence ia i ke kapa sequentially kana olelo hoopomaikai.

Olelo hoopomaikai kau i kekahi waiwai:

- he olelo hoopomaikai ano kekahi ana 'ia;

- paʻa subset mau mai i ka olelo hoopomaikai;

- ana bijection, a ua ho'ākāka 'ia ma luna o ka olelo hoopomaikai pili i ka homeomorphism.

Ano he kumu hoʻohālike olelo hoopomaikai kauʻia e:

- kaupalena 'a paa hou mai la e puhi ia RN;

- finite subsets ma ka hakahaka e like me ka axiom o divisibility T1;

- Theorem Ascoli Arzela characterizing olelo hoopomaikai kau no kekahi ooieoeiiaeuiuo hakahaka;

- Stone wa no i ka holomua Lālā paʻa hōʻailona helu;

- compactification o ka topological pokole.

Noonoo pono i ka ao kau kulana me ka makemakika, kekahi ke hoʻopaʻapaʻa ana i keia mea he lākou i maupaʻa i ka ai iiiaanoaa o nā kumumea me kekahi waiwai. A me kekahi mea hypothetical kau kikowaena likeʻole eiiiiiaiou kūkākūkā manaʻo kūpono. Eia naʻe, kona waiwai i ka mea ku ole i ka loa i loko o ka huapalapala.

Ma ke kahua o ka haʻahaʻa makemakika ao kau ka poe ma ka lākou o integers. Eia naʻe, he kūlana kūikawā e pili ana i kēia 'ia paha ma ka huapalapala kumumanaʻo.

Ka 'ia paha o nā integers ka loaʻa o ka lākou o ka oihana mua (helu) i e ku ae no na maoli ai i helu. Aia i mau hoʻokokoke mai i ka hoomaopopo ana i ka helu maoli:

- hoolilo o 'ikamu (mua, lua, etc.);

- helu o nā kupa (kekahi, i elua, etc.).

Ma kēia hihia, na ole-integers a me ka io integers i keʻano maoli o nui mai e pili. I ka makemakika kahua o ka huapalapala o maoli helu mea N. kēia manaʻo mea ole, i ke aloha a hiki i ke alo o kekahi helu o nā 'ano o nā maoli maoli helu oi aku ia mamua o ka mua.

Haʻalele maoli, i loaa ka helu ma ka manaʻo o ka makemakika ana ma luna o nā helu maoli e like me ka hou 'ole subtraction. Ka 'ia paha o nā integers ma ka makemakika ua koho Z. e unuhi i ka hopena o ka hou a me ka multiplication o nā huahelu o ka helu ana o kekahiʻano wale no ka iaʻano. Ka nele no kēia 'ano o ka hanana nui ma muli o ka nele o ka waiwai, e hooholo i ka likeʻole ma waena o nā integers. He Michael Stifel hoʻolauna i ka makemakika io helu.

Ua pono akahele noonoo i na manaÿo me kana olelo hoopomaikai a puni. Kēia manawa ua hoʻolauna PS Alexandrov e hoʻopuʻipuʻi hou i ka manaʻo o ka olelo hoopomaikai pokole ua hoʻolauna i loko o ka makemakika o Frechet. I ka piha naauao o topological type olelo hoopomaikai mai la, ma ka hihia o finite subcovering kēlā hamama uhi. Ma ka hope kūpono 'ana o ka makemakika, ke kau compactness lilo i mea o ka nui luna ma mua o kona haʻahaʻa counterpart. Ano ka mea, ua maopopo ia e ka compactness compactness, a me ke ano kahiko o ka manawa i loko o ka inoa o "countably kana olelo hoopomaikai." Eia naʻe, nā manaÿo i hua'ōlelo wā hoʻohana 'ia i loko o metric hakahaka.