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
收藏
页码：2411 / 2426
页数：16
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