Weakly Quasi-First-Countable Spaces and Box Products
Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3
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A space $X$ is said to be weakly quasi-first-countable if and only if for all $x \in X$, there exists countably many countable families of decreasing subsets containing $x$ such that a set $O$ is open if and only if for any $x\in O$, $O$ contains a member of each family associated to $x$. For a space $X$, we denote the countable $\sigma$-product of $X$ endowed with the box topology by $\sigma B(X)$. We prove that if $X$ is first-countable and locally compact, then $\sigma B(X)$ is weakly quasi-first-countable, which gives a general method to construct weakly quasi-first-countable spaces which are neither weakly first-countable nor quasi-first-countable.
Classification :
54A05, 54D15
@article{BMMS_2014_37_3_a19,
author = {Rongxin Shen and Fucai Lin},
title = {Weakly {Quasi-First-Countable} {Spaces} and {Box} {Products}},
journal = {Bulletin of the Malaysian Mathematical Society},
year = {2014},
volume = {37},
number = {3},
url = {http://geodesic.mathdoc.fr/item/BMMS_2014_37_3_a19/}
}
Rongxin Shen; Fucai Lin. Weakly Quasi-First-Countable Spaces and Box Products. Bulletin of the Malaysian Mathematical Society, Tome 37 (2014) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2014_37_3_a19/