A NOTE ON CLOSED DISCRETE SUBSETS OF SEPARABLE (a)-SPACES

被引：0

作者：

Morgan, Charles J. G. ^{[1
,2
]}

da Silva, Samuel G. ^{[3
]}

机构：

[1] UCL, Dept Math, London WC1E 6BT, England

[2] Univ Lisbon, Ctr Matemat & Aplicacoes Fundamentais, P-1649003 Lisbon, Portugal

[3] Univ Fed Bahia, Inst Matemat, BR-40170110 Salvador, BA, Brazil

来源：

HOUSTON JOURNAL OF MATHEMATICS | 2012年 / 38卷 / 03期

关键词：

Relative topological properties; locally compact spaces; property (a); countable paracompactness; PROPERTY; SPACES; PRINCIPLES; SEPARATION;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the existence of a T-1 separable space with an uncountable closed discrete subset which satisfies relative versions of property (a) and local compactness implies the existence of small dominating families in the family of functions of omega(1) into omega. Considering well-known relationships between small dominating families and large cardinals, it follows that if Y is an uncountable closed discrete subset of a T-1 separable (a)-space X then there is no way to prove with in ZFC that Y satisfies relative local compactness.

引用

页码：991 / 997

页数：7

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