2005/03/14 by Gary Gruenhage, Gruenhage, Gary
Mathematics · #54D20 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:54D20
paper · pdf · doi:10.48550/arxiv.math/0503275
11 pages
arxiv created 2005/03/14 · arxiv updated 2009/12/01
We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X) is hereditarily a D-space whenever X is a Lindelöf Σ-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact. We also prove that if a space X is the union of finitely many D-spaces, and has countable extent, then X is linearly Lindelöf. It follows that if X is in addition countably compact, then X must be compact. We also show that Corson compact spaces are hereditarily D-spaces. These last two results answer recent questions of Arhangel'skii. Finally, we answer a question of van Douwen by showing that a perfectly normal collectionwise-normal non-paracompact space constructed by R. Pol is a D-space.