Locally compact, monotonically normal Dowker space in ZF plus AD

被引：0

作者：

Burke, Dennis K. ^{[1
]}

机构：

[1] Miami Univ, Dept Math, Oxford, OH 45056 USA

来源：

TOPOLOGY AND ITS APPLICATIONS | 2023年 / 328卷

关键词：

Locally compact; Dowker space; Screenable; Normal; Countably paracompact; Collectionwise normal; Monotonically normal; Baire property; Axiom of determinacy; D-space;

D O I：

10.1016/j.topol.2023.108447

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct a locally compact, monotonically normal, screenable, hereditarily paracompact space Y on P x omega in ZFC. The space Y is also a D-space in ZFC. The space Y is shown to be a locally compact, monotonically normal Dowker space and is not a D-space under ZF+AD and other models of set-theory.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：8

共 13 条

[1] Paracompact in ZFC; CWN screenable Dowker in ZF plus AD
Burke, Dennis K.
TOPOLOGY AND ITS APPLICATIONS, 2022, 312
[2] Normality of products of monotonically normal spaces with compact spaces
Yajima, Yukinobu
TOPOLOGY AND ITS APPLICATIONS, 2011, 158 (15) : 2085 - 2089
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BALOGH, Z
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 323 (01) : 389 - 411
[4] PFA(S)[S] and locally compact normal spaces
Tall, Franklin D.
TOPOLOGY AND ITS APPLICATIONS, 2014, 162 : 100 - 115
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Bennett, Harold R.
Lutzer, David J.
TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (13) : 2218 - 2228
[6] Undecidability for the extent of products of a monotonically normal space and a special factor
Hirata, Yasushi
Yajima, Yukinobu
TOPOLOGY AND ITS APPLICATIONS, 2022, 315
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Pavlov, O
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 129 (09) : 2771 - 2775
[8] On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces
Larson, Paul
Tall, Franklin D.
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2014, 57 (03): : 579 - 584
[9] Locally compact perfectly normal spaces may all be paracompact
Larson, Paul B.
Tall, Franklin D.
FUNDAMENTA MATHEMATICAE, 2010, 210 (03) : 285 - 300
[10] Orthocompactness implies Δ-paracompactness for the product of a Δ-paracompact normal space and a compact space
Hirata, Yasushi
TOPOLOGY AND ITS APPLICATIONS, 2015, 185 : 124 - 133

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