Hauv kev ua lej, qhov chaw me me ntawm qhov chaw topological hu ua tsis muaj qhov ntom ntom lossis tsis tshua muaj yog tias nws kaw muaj qhov khoob sab hauv. Nyob rau hauv ib qho kev xav xoob heev, nws yog ib lub teeb uas nws cov ntsiab lus tsis nruj nruj nyob txhua qhov chaw. Piv txwv li, cov integers tsis muaj qhov ntom ntom ntawm qhov tiag, qhov qhib pob tsis yog.
Is 1 N nowhere ntom?
Ib qho piv txwv ntawm lub teeb uas tsis raug kaw tab sis tseem tsis muaj qhov ntom ntom {1n|
∈N}. Nws muaj ib lub ntsiab lus txwv uas tsis yog nyob rau hauv lub teeb (xws li 0), tab sis nws qhov kaw tseem tsis muaj qhov ntom ntom vim tias tsis muaj qhov qhib qhov sib txawv hauv {1n|n∈N}∪{0}.
Yuav ua li cas ua pov thawj ib lub teeb tsis nyob qhov twg?
A subset A ⊆ X hu ua tsis muaj qhov ntom ntom hauv X yog tias sab hauv ntawm qhov kaw A yog khoob, i.e. (A)◦=∅. Txwv tsis pub, A tsis nyob qhov twg ntom iff nws muaj nyob rau hauv lub kaw kaw nrog khoob sab hauv. Dhau mus ntxiv, peb tuaj yeem hais sib npaug tias A tsis nyob qhov twg ntom ntom iff nws cov khoom ntxiv muaj cov txheej qhib ntom ntom (vim li cas?).
Txhua qhov chaw ntom ntom txhais li cas?
A subset A ntawm qhov chaw topological X yog qhov ntom ntom rau qhov qhov kaw yog tag nrho qhov chaw X (qee tus kws sau ntawv siv cov lus nyob txhua qhov chaw ntom ntom). Ib qho kev txhais lwm txoj hauv kev yog: lub teeb A uas cuam tshuam txhua qhov tsis muaj qhov qhib subset ntawm X.
Puas yog txhua qhov qhib qhib?
A topological space X yog hyperconnected yog tias thiab tsuas yog txhua qhov tsis muaj npe qhibteeb tsa ntom ntom hauv X. Ib qhov chaw topological yog submaximal yog tias thiab tsuas yogtxhua qhov ntom ntom tau qhib.
