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Summary
We introduce the class of S-paracompact spaces as a generalization of paracompact spaces. A space (X,T) is S-paracompact if every open cover of X has a locally finite semi-open refinement. We characterize S-paracompact spaces and study their basic properties. The relationships between S-paracompact spaces and other well-known spaces are investigated.
Abstract
Some characterizations of S-paracompact spaces are given. We introduce a class of S-expandable spaces and study topological properties of S-expandable spaces.
Abstract
We continue to study the characterizations of paracompact locally compact spaces under certain quotient mappings, and discuss the relationships among them, which expand the results on certain quotient images of paracompact locally compact spaces.
Paracompactness revisited Appl. Cat. Structures 1 181 – 190 10.1007/BF00880042 . [5] Banaschewski , B. , Pultr , A. 1996 Cauchy points of uniform and nearness frames Quaest. Math. 19 101 – 127 10
In a topological spaceX, a T2-distinct pointx means that for anyy∈X x≠y, there exist disjoint open neighbourhoods ofx andy. Similarly, T0-distinct points and T1distinct points are defined. In a Ti-distinct point-setA, we assume that eachx∈A is a T i -distinct point (i=0, 1, 2). In the present paper some implications of these notions which ‘localize’ the T i -separation axioms (i=0, 1, 2) requirement, are studied. Suitable variants of regularity and normality in terms of T2-distinct points are shown hold in a paracompact space (without the assumption of any separation axioms). Later T0-distinct points are used to give two characterizations of the R D -axiom.1 In the end, some simple results are presented including a condition under which an almost compact set is closed and a result regarding two continuous functions from a topological space into a Hausdorff space is sharpened. A result which relates a limit pointv to an ω-limit point is stated.
Abstract
We show that a monotonically normal space X is paracompact if and only if for every increasing open cover {U α : α < κ} of X, there is a closed cover {F nα : n < ω, α < κ} of X such that F nα ⊂ U α for n < ω, α < κ and F nα ⊂ F nβ if α ≦ β.
. 1951 On countably paracompact spaces Canad. J. Math. 3 219 – 224 10.4153/CJM-1951-026-2 . [4] Engelking , R
