Indestructibility of compact spaces

被引：5

作者：

Dias, Rodrigo R. ^{[1
,2
]}

Tall, Franklin D. ^{[3
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, BR-05314970 Sao Paulo, Brazil

[2] Minist Educ Brazil, Capes Fdn, BR-70040020 Brasilia, DF, Brazil

[3] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

TOPOLOGY AND ITS APPLICATIONS | 2013年 / 160卷 / 18期

关键词：

Compact; Indestructible; Selection principles; Topological games; Inaccessible cardinal; Borel's Conjecture; TOPOLOGICAL GAMES; CARDINALITY;

D O I：

10.1016/j.topol.2013.07.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to omega(1)-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba's "N-1-Borel Conjecture" is equiconsistent with the existence of an inaccessible cardinal. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：2411 / 2426

页数：16

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