Yaying'ono akonzedwa

Yaying'ono akonzedwa ndi topological danga akufotokozera chivundikiro amene ali amalire subcover. mipata yaying'ono mu mtunda wa katundu wawo, amakhala ngati dongosolo kukukhala amalire chiphunzitso chogwirizana.

Yaying'ono akonzedwa kapena CD - ndi kagawo wa danga topological, amene anachititsa ndi mtundu wa danga yaying'ono.

Poyamba chimaoneka (precompact) wayikidwa okha nkhani ya dera yaying'ono. Pamene Kupeleka malo mu subsequence convergent kuti angatchedwe sequentially yaying'ono.

Yaying'ono akonzedwa ali katundu chindunji:

- m'njira yaying'ono anasonyeza iliyonse mosalekeza;

- chatsekedwa kagawo nthawi zonse ali ndi yaying'ono;

- mosalekeza bijection, amene anafotokozedwa pa yaying'ono ndi amatanthauza homeomorphism.

Zitsanzo yaying'ono akonzedwa ndi:

- okha ndi kutsekedwa waika RN;

- subsets amalire mu mipata kuti agwirizane axiom wa divisibility T1;

- Lingaliro Lovomerezeka Ascoli Arzela amakhala yaying'ono anasiyira ena mipata zinchito;

- Stone malo a ajebura Buliyani;

- compactification wa danga topological.

Poganizira chilengedwe amaika malo ndi masamu, munthu anganene kuti uwu ndi akonzedwa zomwe zizindikiro kuchuluka kwa zinthu ndi katundu yeniyeni. Pamodzi ndi china Wonenedwa zikuphatikizapo zosiyanasiyana zigawo zikuluzikulu takambirana mfundo alipo. Komabe, katundu ndi zosiyana ndi chofunikira kwambiri kwa Anatipatsa.

M'munda wa pulayimale masamu akonzedwa chilengedwe ukufanizidwa ndi ya integers. Komabe, udindo wapadera limabweretsa akonzedwa izi chiphunzitso akonzedwa.

Achikhalire a integers zikuphatikizapo ya zinthu (manambala) amene angakhalepo mwachibadwa pa kuwerenga. Pali njira ziwiri kudziwa manambala chachilengedwe:

- kulanda zinthu (choyamba, chachiwiri, etc.);

- chiwerengero cha nkhani (mmodzi, ziwiri, etc.).

Pankhaniyi, osiyanasiyana amene sanali integers ndi integers zoipa mtundu zachilengedwe manambala sizikhudza. M'munda masamu wa ya manambala zachilengedwe ndi N. Mfundo imeneyi wosatha, chifukwa kukhalapo kwa chiwerengero cha mitundu ina ya zachilengedwe chiwerengero zachilengedwe woposa woyamba.

Mosiyana zachilengedwe, manambala lonse akamagwira kukhazikitsa ntchito masamu pa manambala zachilengedwe monga Kuwonjezera kapena wochotsera. Achikhalire a integers mu masamu ndi anatchulidwa Z. Mwa Kuchotsera zotsatira za Kuwonjezera ndi chulutsa manambala awiri ndi chiwerengero cha mtundu okha wa mtundu womwewo. Kufunika kwa mtundu uwu wa nambala yatsoka chifukwa satha kudziwa kusiyana pakati integers awiri. Ndi Michael Stifel anaphunzitsidwa Masamu manambala negative.

Pamafunika mosamala mfundo monga malo yaying'ono. Mawu amenewa anayambitsa PS Alexandrov kuti ya limbitse chiphunzitso cha malo yaying'ono umayamba mu masamu a Frechet. The bwinobwino wa topological mtundu danga yaying'ono ngati amalire subcovering lililonse chophimba lotseguka. Mu chitukuko wotsatira wa masamu, mawu compactness anakhala dongosolo la udzakwaniritsidwa kuposa mnzake ake m'munsi. Ndipo tsopano anamvetsa ndi compactness compactness, ndi ubale akale akuti ali mutu wa "countably yaying'ono." Komabe, mfundo onse ali ofanana pamene ntchito mipata chinkafunika.