# ON TOTALLY PARACOMPACT METRIC SPACES

@inproceedings{Lelek1968ONTP,
title={ON TOTALLY PARACOMPACT METRIC SPACES},
author={A. Lelek},
year={1968}
}
A topological space is said to be totally paracompact [4] if every open basis contains a locally finite cover. It is known [2] that no reflexive infinite-dimensional Banach space is totally paracompact. It is also known [1], [3] that the space of irrationals with usual topology is not totally paracompact. In the present paper we prove a theorem which gives a necessary condition in order that a subset of a complete metric space be totally paracompact. This allows us to exhibit some pathology… Expand
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