PFA(S) [S] and countably compact spaces

被引：3
作者：
Dow, Alan [1 ]
Tall, Franklin D. [2 ]
机构：
[1] Univ N Carolina, Dept Math & Stat, Charlotte, NC 28223 USA
[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
来源：
TOPOLOGY AND ITS APPLICATIONS | 2017年 / 230卷
基金：
美国国家科学基金会; 加拿大自然科学与工程研究理事会;
关键词：
Locally compact; Normal; Countably compact; Free sequence; Countably tight; Coherent Souslin tree; PFA(S) [S; Perfect pre-image of omega(1); Paracompact; Sequentially compact; SOUSLIN TREE;
D O I：
10.1016/j.topol.2017.08.021
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show a number of undecidable assertions concerning countably compact spaces hold under PFA(S) [S]. We also show the consistency without large cardinals of every locally compact, perfectly normal space is paracompact. (C) 2017 Elsevier B.V. All rights reserved.
引用
收藏
页码：393 / 416
页数：24
相关论文
共 50 条
  • [21] When a compact (countably compact) set is closed
    G. L. Garg
    N. Singh
    Acta Mathematica Hungarica, 2002, 94 (3) : 233 - 239
  • [22] A non-pseudocompact product of countably compact spaces via Seq
    Lindgren, WF
    Szymanski, AA
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (12) : 3741 - 3746
  • [23] When a compact (countably compact) set is closed II
    Garg L.
    Singh N.
    Acta Mathematica Hungarica, 2004, 105 (4) : 331 - 337
  • [24] When a compact (countably compact) set is closed. II
    Garg, GL
    Singh, N
    ACTA MATHEMATICA HUNGARICA, 2004, 105 (04) : 331 - 337
  • [25] Between countably compact and ω-bounded
    Juhasz, Istvan
    Soukup, Lajos
    Szentmiklossy, Zoltan
    TOPOLOGY AND ITS APPLICATIONS, 2015, 195 : 196 - 208
  • [26] Normality Versus Paracompactness in Locally Compact Spaces
    Dow, Alan
    Tall, Franklin D.
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2018, 70 (01): : 74 - 96
  • [27] The gap between the dimensions of countably paracompact spaces
    Charalambous, Michael G.
    TOPOLOGY AND ITS APPLICATIONS, 2008, 155 (17-18) : 2216 - 2220
  • [28] Locally compact, ω1-compact spaces
    Nyikos, Peter
    Zdomskyy, Lyubomyr
    ANNALS OF PURE AND APPLIED LOGIC, 2024, 175 (01)
  • [29] On the product of a compact space with an absolutely countably compact space
    Vaughan, JE
    PAPERS ON GENERAL TOPOLOGY AND APPLICATIONS: TENTH SUMMER CONFERENCE AT AMSTERDAM, 1996, 788 : 203 - 208
  • [30] Countably compact hyperspaces and Frolik sums
    Juhasz, Istvan
    Vaughan, Jerry E.
    TOPOLOGY AND ITS APPLICATIONS, 2007, 154 (12) : 2434 - 2448
12345