Base-cover paracompactness

Popvassilev, Strashimir

doi:10.1090/S0002-9939-04-07457-X

Base-cover paracompactness
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by Strashimir G. Popvassilev

Proc. Amer. Math. Soc. 132 (2004), 3121-3130

DOI: https://doi.org/10.1090/S0002-9939-04-07457-X

Published electronically: May 12, 2004

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Abstract:

Call a topological space $X$ base-cover paracompact if $X$ has an open base $\mathcal {B}$ such that every cover $\mathcal {C}\subset \mathcal {B}$ of $X$ contains a locally finite subcover. A subspace of the Sorgenfrey line is base-cover paracompact if and only if it is $F_\sigma$. The countable sequential fan is not base-cover paracompact. A paracompact space is locally compact if and only if its product with every compact space is base-cover paracompact.

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