A space $X$ is said to be {\it strongly base-paracompact\/} if there is a basis $\Cal B$ for $X$ with $|\Cal B|=w(X)$ such that every open cover of $X$ has a star-finite open refinement by members of $\Cal B$. Strongly paracompact spaces which are strongly base-paracompact are studied. Strongly base-paracompact spaces are shown have a family of functions $\Cal{F}$ with cardinality equal to the weight such that every open cover has a locally finite partition of unity subordinated to it from $\Cal F$.
@article{119387,
author = {John E. Porter},
title = {Strongly base-paracompact spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {44},
year = {2003},
pages = {307-314},
zbl = {1099.54021},
mrnumber = {2026165},
language = {en},
url = {http://dml.mathdoc.fr/item/119387}
}
Porter, John E. Strongly base-paracompact spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 44 (2003) pp. 307-314. http://gdmltest.u-ga.fr/item/119387/
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