On spaces with $σ$-closed discrete dense sets

Rodrigo R. Dias, Daniel T. Soukup

Published 2017-01-02Version 1

The main purpose of this paper is to study $e$-separable spaces, originally introduced by Kurepa as $K_0'$ spaces; a space $X$ is $e$-separable iff $X$ has a dense set which is the union of countably many closed discrete sets. We primarily focus on the behaviour of $e$-separable spaces under products and the cardinal invariants that are naturally related to $e$-separable spaces. Our main results show that the statement "the product of at most $\mathfrak c$ many $e$-separable spaces is $e$-separable" depends on the existence of certain large cardinals and hence independent of ZFC.