Geodesic
A covering criterion and its applications to product theorems
Commentationes Mathematicae, Tome 45 (2005) no. 1, pp. 33-41.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/cm.v45i1.5226
Mots-clés : Compact space, Tychonoff’s product theorem, Lindelöf space, ideal of sets 
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Jacek Jachymski. A covering criterion and its applications to product theorems. Commentationes Mathematicae, Tome 45 (2005) no. 1, pp.  33-41. doi : 10.14708/cm.v45i1.5226. http://geodesic.mathdoc.fr/articles/10.14708/cm.v45i1.5226/

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