Remarks on w-domination of discrete subspaces

Abstract

Given a space X, we will say that a class A of subsets of X is dominated by a class B if for any A ∈ A, there exists a B ∈ B such that A ⊂ B̅. In particular, all (closed) discrete subsets of X are countably dominated (which we frequently abbreviate as w-dominated) if, for any (closed) discrete set D ⊂ X, there exists a countable set B ⊂ X such that D ⊂ B̅. In this paper, we investigate the topological properties of spaces in which (closed) discrete subspaces are dominated either by countable subsets or by Lindelöf subspaces.

Mathematics Subject Classification (2010): Primary 54D20, 54A25; Secondary 54A35.

Keywords: w-domination of discrete subsets, G_δ-diagonal, star Lindelöf, semi-stratifiable space