Bella, Angelo The density topology is extraresolvable. (English) Zbl 1013.54001 Atti Semin. Mat. Fis. Univ. Modena 48, No. 2, 495-498 (2000). Let us recall that for a space \(X\), the dispersion character \(\Delta(X)\) is the smallest cardinality of a non-empty open subset of \(X\). A space \(X\) is said to be extraresolvable if there is a family \(\mathcal D\) of dense subsets of \(X\) such that \(|\mathcal D|>\Delta(X)\) and \(D\cap D'\) is nowhere dense whenever \(D,D'\in\mathcal D\) and \(D\neq D'\). It is easy to see that the real line with the Euclidean topology is not extraresolvable. The author proves that under Martin’s axiom the real line with the Lebesgue density topology is extraresolvable. Reviewer: Miroslav Repický (Kosice) Cited in 1 Review MSC: 54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets) 03E50 Continuum hypothesis and Martin’s axiom Keywords:\(\kappa\)-resolvable space; maximally resolvable space; extraresolvable space; Martin’s axiom; Lebesgue density topology PDFBibTeX XMLCite \textit{A. Bella}, Atti Semin. Mat. Fis. Univ. Modena 48, No. 2, 495--498 (2000; Zbl 1013.54001)