paracompact space

(redirected from Paracompactness)

paracompact space

[¦par·ə¦käm‚pakt ‚spās]
(mathematics)
A topological space with the property that every open covering F is associated with a locally finite open covering G, such that every element of G is a subset of an element F.
References in periodicals archive ?
Hou, "Existence of equilibria for generalized games without paracompactness" Nonlinear Analysis.
Tkachuk and Wilson showed in the paper [18] that paracompactness and the Lindelof property are both discretely reflexive in GO spaces.
Reilly, On some strong forms of paracompactness, Q & A in general topology, 5(1987), 303-310.
The first seven chapters cover the usual topics of point-set or general topology, including topological spaces, new spaces from old ones, connectedness, the separation and countability axioms, and metrizability and paracompactness, as well as special topics such as contraction mapping in metric spaces, normed linear spaces, the Frechet derivative, manifolds, fractals, compactifications, the Alexander subbase, and the Tychonoff theorems.
The notion of paracompactness in ideals was initiated by Hamlett et al [6] in the year 1997.
(iii) If [G.sub.1] and [G.sub.2] are two grills on a space with [G.sub.1] C [G.sub.2], then [G.sub.2]-[theta]- paracompactness of X ft [G.sub.1]-[theta]-paracompactness of X.
(iv) Considering G [theta] paracompactness, refinement need not be a cover.
By G-[theta]- paracompactness of (X, [tau]), U has a [tau] locally finite [tau] [theta]-open precise refinement V = {[V.sub.[alpha]]: [alpha] [member of] [LAMBDA]} such that X\([[union].sub.[alpha][member of][LAMBDA]][V.sub.[alpha]])[??] G.
It is well-known that in generalized ordered spaces the D-property is equivalent to paracompactness ([6]).
It happens that for P = paracompactness (resp., metrizability, Lindelofness and quasi-developability) a generalized ordered space has P if and only if its (minimal) closed linearly ordered extension has P.
In [6] it is shown that in generalized ordered spaces the D-property is equivalent to paracompactness, and thus l(M) is a hereditary D-space.
O'Meara, On paracompactness in function spaces with the compact-open topology, Proc.