A covering criterion and its applications to product theorems

• Autorzy: Jachymski J.
• Języki publikacji: EN

Abstrakty

EN

We establish a covering criterion involving a neighbourhood system and idealsof open sets which yields,in particular, a compactness criterion for an arbitrary topologicalspace. As an application, we give new proofsof Tychonoff's compactness theorem: we consider separately the case of acountable product, in a proof of which the ordinary mathematical induction isused, and the case of an uncountable product proved by the transfiniteinduction. Subsequently, the same argument is applied to obtain some resultson products of Lindelöf spaces.

Słowa kluczowe

EN

compact space; Tychonoff's product theorem; Lindel's of space; ideal of sets

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2005
• Tom: Vol. 45, [Z] 1
• Strony: 35--43
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Jachymski J.

• Institute of Mathematics, Technical University of Łódź,

Bibliografia

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