Finite Unions of D-Spaces and Applications of Nearly Good Relation. (24th April 2013)

• Record Type: Journal Article
• Authors: Zhang, Xin; Guo, Hongfeng; Xu, Yuming
• Other Names: Xu Fuyi Academic Editor.
• Is Part Of: Discrete dynamics in nature and society. Volume 2013(2013)
• Publication Date: 2013-04-24
• Subjects: System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/2013/808262
• Languages: English
• ISSNs: 1026-0226

Abstract

Abstract : 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.