Selective separability and q⁺ on maximal spaces

2020/01/20 by de la Vega, Ramiro, Murgas, Javier, Uzcátegui, Carlos
#03E57 #54A35 #54G05 #FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.2001.07156

Abstract

Given a hereditarily meager ideal I on a countable set X we use Martin's axiom for countable posets to produce a zero-dimensional maximal topology τ^I on X such that τ^I∩ I=\∅\ and, moreover, if I is p⁺ then τ^I is selectively separable (SS) and if I is q⁺, so is τ^I. In particular, we obtain regular maximal spaces satisfying all boolean combinations of the properties SS and q⁺.

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