Finite Unions of D-Spaces and Applications of Nearly Good Relation

Some results are obtained on finite unions of D-spaces. It is proved that if a space is the union of finitely many locally compact D-subspaces, then it is a D-space. It follows that a space is a D-space if it is the union of finitely many locally compact submetacompact subspaces. And a space is a D-...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2013-01, Vol.2013 (2013), p.114-117
Main Authors: Zhang, Xin, Guo, Hongfeng, Xu, Yuming
Format: Article
Language:English
Subjects:
Dynamics
Mathematical analysis
Mathematical research
Neighborhoods
Subspaces
Topological spaces
Unions
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Summary:Some results are obtained on finite unions of D-spaces. It is proved that if a space is the union of finitely many locally compact D-subspaces, then it is a D-space. It follows that a space is a D-space if it is the union of finitely many locally compact submetacompact subspaces. And a space is a D-space if it is the union of a D-subspace with a locally compact D-subspace. This partially answers one problem raised by Arhangel’skii. At last, some examples are given to exhibit the applications of nearly good relation to discover D-classes.
ISSN:1026-0226
1607-887X
DOI:10.1155/2013/808262