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On the extent of separable, locally compact, selectively (a)-spaces

Samuel G. da Silva — 2015

Colloquium Mathematicae

The author has recently shown (2014) that separable, selectively (a)-spaces cannot include closed discrete subsets of size . It follows that, assuming CH, separable selectively (a)-spaces necessarily have countable extent. However, in the same paper it is shown that the weaker hypothesis " 2 ℵ ₀ < 2 ℵ ₁ " is not enough to ensure the countability of all closed discrete subsets of such spaces. In this paper we show that if one adds the hypothesis of local compactness, a specific effective (i.e., Borel) parametrized...

On star covering properties related to countable compactness and pseudocompactness

Marcelo D. Passos;  Heides L. Santana;  Samuel G. da Silva — 2017

Commentationes Mathematicae Universitatis Carolinae

We prove a number of results on star covering properties which may be regarded as either generalizations or specializations of topological properties related to the ones mentioned in the title of the paper. For instance, we give a new, entirely combinatorial proof of the fact that Ψ -spaces constructed from infinite almost disjoint families are not star-compact. By going a little further we conclude that if X is a star-compact space within a certain class, then X is neither first countable nor separable....

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