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totally paracompact

Last-modified: 2010-09-06 (月) 17:10:14

Definition 1 Edit

A space is said to be totally paracompact if every open base has a locally finite subfamily covering the space.

Definition 2 Edit

Let X be a topological space and let Y be its subset.
Y is called totally paracompact with respect to X if every outer base contains a X-locally finite cover. A family B of open sets in X is called an outer cover if, for every point y in Y and every open set G in X, there is some member V of B such that x is contained in V and that V is contained in G.

Remark Edit

Reference Edit

Definition 1
R. M. Ford, Basic properties in dimension theory, Dissertation, Auburn University, 1963.
M. K. Singal, Some Generalizations of Paracompactness, Proceedings of the Kanpur topological conference, 1968. Academia Publishing House of the Czechoslovak Academy of Sciences, Praha, 1971. pp. 245-263.
Definition 2
R. Telgarsky and H. Kok, The space of rationals is not absolutely paracompact, Fund. Math. 73 (1971), 75-78.