ON THE CARDINALITY OF COUNTABLE DENSE HOMOGENEOUS SPACES

被引：8

作者：

Arhangel'skii, A. V. ^{[1
]}

van Mill, J. ^{[2
]}

机构：

[1] Ohio Univ, Dept Math, Athens, OH 45701 USA

[2] Vrije Univ Amsterdam, Fac Sci, Dept Math, NL-1081 HV Amsterdam, Netherlands

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2013年 / 141卷 / 11期

关键词：

Countable dense homogeneous; cardinality; Continuum Hypothesis;

D O I：

10.1090/S0002-9939-2013-11649-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a countable dense homogeneous space has size at most continuum. If moreover it is compact, then it is first-countable under the Continuum Hypothesis. We also construct under the Continuum Hypothesis an example of a hereditarily separable, hereditarily Lindelof, countable dense homogeneous compact space of uncountable weight.

引用

页码：4031 / 4038

页数：8

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