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- W2156012228 abstract "A topological space is paracompact if and only if each open cover of the space has an open locally finite refinement. It is well-known that an unusual normality condition is satisfied by each paracompact regular space X [p. 158, 5]: Let α be a locally finite (discrete) family of subsets of X , then there is a neighborhood V of the diagonal Δ( X ) (in X × X ), such that V [ x ] intersects at most a finite number of members (respectively at most one member) of { V [ A ]: A ∈ α} for each x ∈ X . In this not we will show that a variant of this condition actually characterizes paracompactness. Among other results, an improvement to a recent result of H. H.Corson [2] is given so as to accord with a conjecture of J. L. Kelley [p. 208, 5] more prettily, and we connect paracompactness to metacompactness [1]" @default.
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- W2156012228 date "1961-10-01" @default.
- W2156012228 modified "2023-09-27" @default.
- W2156012228 title "On paracompact regular spaces" @default.
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- W2156012228 doi "https://doi.org/10.1017/s1446788700026628" @default.
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