A covering criterion and its applications to product theorems

Jacek Jachymski. "A covering criterion and its applications to product theorems." Commentationes Mathematicae 45.1 (2005): null. <http://eudml.org/doc/291915>.

@article{JacekJachymski2005,
abstract = {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.},
author = {Jacek Jachymski},
journal = {Commentationes Mathematicae},
keywords = {Compact space; Tychonoff’s product theorem; Lindelöf space; ideal of sets},
language = {eng},
number = {1},
pages = {null},
title = {A covering criterion and its applications to product theorems},
url = {http://eudml.org/doc/291915},
volume = {45},
year = {2005},
}

TY - JOUR
AU - Jacek Jachymski
TI - A covering criterion and its applications to product theorems
JO - Commentationes Mathematicae
PY - 2005
VL - 45
IS - 1
SP - null
AB - 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.
LA - eng
KW - Compact space; Tychonoff’s product theorem; Lindelöf space; ideal of sets
UR - http://eudml.org/doc/291915
ER -