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• # Artykuł - szczegóły

## Colloquium Mathematicum

2015 | 141 | 2 | 199-208

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

EN

### Abstrakty

EN
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.

199-208

wydano
2015

### Twórcy

autor
• Instituto de Matemática, Universidade Federal da Bahia, Av. Adhemar de Barros, S/N, Ondina, CEP 40170-110, Salvador, BA, Brazil