Finite Unions of D-Spaces and Applications of Nearly Good Relation. (24th April 2013) - Zhang, Xin; Guo, Hongfeng; Xu, Yuming
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.