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

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da Silva S.

Colloquium Mathematicum

2015

tom 141

nr 2

199-208

The author has recently shown (2014) that separable, selectively (a)-spaces cannot include closed discrete subsets of size 𝔠. 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 "$2^{ℵ₀} < 2^{ℵ₁}$" 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.

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1 Colloquium Mathematicum

1 da Silva S.

1 2015

Wyniki wyszukiwania

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