When is a P-space weakly discretely generated?

A space X is discretely generated at a point x∈X if for any A⊆X with x∈cl(A), there exists a discrete set D⊆A such that x∈cl(D). The space X is discretely generated if it is discretely generated at every point x∈X. We say that X is weakly discretely generated if for any non-closed set A⊆X, there exi...

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Bibliographic Details
Published in:Topology and its applications 2014-02, Vol.163, p.2-10
Main Authors: Alas, Ofelia T., Junqueira, Lucia R., Wilson, Richard G.
Format: Article
Language:English
Subjects:
Countable extent
Discretely generated space
Fréchet net character
Lindelöf space
P-space
Weakly discretely generated space
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Summary:A space X is discretely generated at a point x∈X if for any A⊆X with x∈cl(A), there exists a discrete set D⊆A such that x∈cl(D). The space X is discretely generated if it is discretely generated at every point x∈X. We say that X is weakly discretely generated if for any non-closed set A⊆X, there exists a discrete set D⊆A such that cl(D)\A≠∅. We obtain new results concerning these properties in the class of P-spaces.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2013.10.001