A note on D-spaces☆
By Gary Gruenhage. 2005
54 citations recorded by the source corpus.
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 Lindelof 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 Lindelof. 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d81e212a4743ed0520b5a43627da04f6f5f8798c
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- A survey of D-spaces (2010, methodology): “In [32], I used the idea of stickyness to argue that in many cases to show that a space is a D-space, one only has to produce a single nonempty closed discrete sticky subset D of an arb itrary nonempty closed subspace F .”