Extraresolvability and cardinal arithmetic
A Tikhonov space \(X\) without isolated points is said to be extraresolvable (by Malykhin) if it contains a system \(\mathcal D\) of dense subsets such that two members of \(\mathcal D\) intersect in a nowhere dense set and \(|{\mathcal D}|\) is bigger than the least cardinality \(\Delta X\) of a nonempty open subset of \(X\). Extraresolvability of certain products and of generalized \(\Sigma \)-products depend on cardinal arithmetic. It is also shown that there are compact extraresolvable spaces \(X\) with \(|X|=\Delta \), \(X=2^\kappa \), and extraresolvable topological Abelian groups having various properties.
scientific article; zbMATH DE number 1682890
scientific article