DMS Set Theoretic Topology Seminar

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.