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

Samuel G. da Silva

Colloquium Mathematicae (2015)

  • Volume: 141, Issue: 2, page 199-208
  • ISSN: 0010-1354

Abstract

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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 weak diamond principle implies countable extent in this context.

How to cite

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Samuel G. da Silva. "On the extent of separable, locally compact, selectively (a)-spaces." Colloquium Mathematicae 141.2 (2015): 199-208. <http://eudml.org/doc/284227>.

@article{SamuelG2015,
abstract = {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 "$2^\{ℵ₀\} < 2^\{ℵ₁\}$" 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.},
author = {Samuel G. da Silva},
journal = {Colloquium Mathematicae},
keywords = {locally compact spaces; star covering properties; property $(a)$; selection principles; selectively $(a)$; parametrized diamond principles},
language = {eng},
number = {2},
pages = {199-208},
title = {On the extent of separable, locally compact, selectively (a)-spaces},
url = {http://eudml.org/doc/284227},
volume = {141},
year = {2015},
}

TY - JOUR
AU - Samuel G. da Silva
TI - On the extent of separable, locally compact, selectively (a)-spaces
JO - Colloquium Mathematicae
PY - 2015
VL - 141
IS - 2
SP - 199
EP - 208
AB - 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 "$2^{ℵ₀} < 2^{ℵ₁}$" 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.
LA - eng
KW - locally compact spaces; star covering properties; property $(a)$; selection principles; selectively $(a)$; parametrized diamond principles
UR - http://eudml.org/doc/284227
ER -

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