On cellular-compact spaces

Abstract

As it was introduced by Tkachuk and Wilson in [7], a topological space X is cellular-compact if for any cellular, i.e. disjoint, family $$\mathcal{U}$$ of non-empty open subsets of X there is a compact subspace $$K \subset X$$ such that $$K \cap U \ne \emptyset$$ for each $$U \in \mathcal{U}$$ . In this note we answer several questions raised in [7] by showing that