COSAM » Events » 2020 » February » DMS Set Theoretic Topology Seminar

 DMS Set Theoretic Topology Seminar Time: Feb 14, 2020 (02:00 PM) Location: Parker Hall 246 Details: Speaker: Professor Vladimir Tkachuk Title: A countable space need not be weakly discretely generated Abstract: We will construct a countable crowded Tychonoff space $$X$$ in which all discrete subsets are closed. This very non-trivial example of van Douwen shows that a discretely metrizable space is not necessarily first countable or even Frechet-Urysohn. This space has no non-trivial convergent sequences, every dense subspace of $$X$$ is open and every nowhere dense subset of $$X$$ is closed and discrete.

Last updated: 02/13/2020