Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9517001 | Topology and its Applications | 2005 | 13 Pages |
Abstract
Among new results, it is proved that if a linearly ordered space is an aD-space, then it is paracompact. The statement further extends the list of equivalences in [Proc. Amer. Math. Soc. 125 (1997) 1237]. We also establish some sufficient conditions for the free topological group of a Tychonoff space to be a D-space. In particular, the free topological group of a semi-stratifiable space is shown to be a D-space, while it need not be semi-stratifiable. A similar result is established for the free topological group of a space with a point-countable base. Some new interesting open problems on D-spaces and on spaces close to them are formulated. In particular, we discuss several such questions in connection with the sum theorems.
Related Topics
Physical Sciences and Engineering
Mathematics
Geometry and Topology
Authors
Alexander V. Arhangel'skii,