Geodesic
D-Spaces and Resolution
Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 395-401

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DOI

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 Y x 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.
DOI : 10.4153/CMB-1997-047-5
Mots-clés : Primary: 54D20, 54B99, secondary: 54D10, 54D30, D-space, neighborhood assignment, resolution, boundary 
Boudhraa, Zineddine. D-Spaces and Resolution. Canadian mathematical bulletin, Tome 40 (1997) no. 4, pp. 395-401. doi: 10.4153/CMB-1997-047-5
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     title = {D-Spaces and {Resolution}},
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     year = {1997},
     volume = {40},
     number = {4},
     doi = {10.4153/CMB-1997-047-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-047-5/}
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