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 "" 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 weak diamond principle implies countable extent in this context.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-5,
author = {Samuel G. da Silva},
title = {On the extent of separable, locally compact, selectively (a)-spaces},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {199-208},
zbl = {06487238},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-5}
}
Samuel G. da Silva. On the extent of separable, locally compact, selectively (a)-spaces. Colloquium Mathematicae, Tome 139 (2015) pp. 199-208. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-5/