A note on D-spaces
| dc.creator | Gruenhage, Gary | |
| dc.date | 2005-03-14 | |
| dc.date.accessioned | 2026-07-07T05:17:56Z | |
| dc.date.available | 2026-07-07T05:17:56Z | |
| dc.description | 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 C_p(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. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/math/0503275 | |
| dc.identifier | http://arxiv.org/abs/math/0503275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74489 | |
| dc.subject | General Topology | |
| dc.subject | 54D20 | |
| dc.title | A note on D-spaces | |
| dc.type | text |