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D-Spaces and Resolution

Published online by Cambridge University Press:  20 November 2018

Zineddine Boudhraa
Zineddine Boudhraa*
Affiliation:
Bowie State University, Department of Mathematics, Bowie, Maryland 20715, U.S.A., e-mail: boudhraa@mcs.kent.edu
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Abstract

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A space X is a D-space if, for every neighborhood assignment f there is a closed discrete set D such that f(D) = X. In this paper we give some necessary conditions and some sufficient conditions for a resolution of a topological space to be a D-space. In particular, if a space X is resolved at each x ∊ X into a D-space Yx by continuous mappings fx: X − {x} → Yx, then the resolution is a D-space if and only if {x} × Bd(Yx) is a D-space.

Keywords

Primary: 54D2054B99secondary: 54D1054D30D-spaceneighborhood assignmentresolutionboundary
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 395 - 401
Copyright
Copyright © Canadian Mathematical Society 1997

References

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3. Watson, S., The Construction of Topological Spaces. Recent Progress in General Topology, North-Holland, 1992.Google Scholar