A covering criterion and its applications to product theorems

• Autorzy: Jacek Jachymski
• Języki publikacji: EN

Abstrakty

EN

We establish a covering criterion involving a neighbourhood system and ideals of open sets which yields, in particular, a compactness criterion for an arbitrary topological space. As an application, we give new proofs of Tychonoff’s compactness theorem: we consider separately the case of a countable product, in a proof of which the ordinary mathematical induction is used, and the case of an uncountable product proved by the transfinite induction. Subsequently, the same argument is applied to obtain some results on products of Lindelöf spaces.

Słowa kluczowe

EN

Compact space; Tychonoff’s product theorem; Lindelöf space; ideal of sets

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2005
• Tom: 45
• Numer: 1

Daty

wydano

2005

online

2017-12-19

Twórcy

autor

Jacek Jachymski

Identyfikatory

DOI

10.14708/cm.v45i1.5226