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Maximally resolvable lower density spaces. (English) Zbl 1159.28001

Authors’ abstract: It is shown that all measure based and all category based lower density topologies on \({\mathcal R}\) are maximally resolvable in ZFC and extraresolvable under ZFC + MA. It is also noted that both maximal resolvability and extraresolvability are feeble topological properties.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies)
54C08 Weak and generalized continuity
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