Compact monotonically metacompact spaces are metrizable

被引：11
|
作者：
Chase, Timothy [1 ]
Gruenhage, Gary [1 ]
机构：
[1] Auburn Univ, Dept Math, Auburn, AL 36830 USA
来源：
TOPOLOGY AND ITS APPLICATIONS | 2013年 / 160卷 / 01期
关键词：
Monotonically (countably) metacompact; Metrizable; Single ultrafilter space;
D O I：
10.1016/j.topol.2012.09.011
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Monotonically metacompact spaces were recently introduced as an extension of the concept of monotonically compact spaces. In this note we answer a question of Popvassilev, and Bennett, Hart, and Lutzer, by showing that every compact, Hausdorff, monotonically (countably) metacompact space is metrizable. We also show that certain countable spaces fail to be monotonically (countably) metacompact. (C) 2012 Elsevier By. All rights reserved.
引用
收藏
页码：45 / 49
页数：5
相关论文
共 50 条
  • [1] A RESULT ON MONOTONICALLY METACOMPACT SPACES
    Xu, Ai-Jun
    Shi, Wei-Xue
    HOUSTON JOURNAL OF MATHEMATICS, 2013, 39 (04): : 1437 - 1442
  • [2] A Note on Monotonically Metacompact Spaces
    Hui LI
    Liangxue PENG
    数学研究及应用, 2013, 33 (03) : 353 - 360
  • [3] A note on monotonically metacompact spaces
    Bennett, Harold R.
    Hart, Klaas Pieter
    Lutzer, David J.
    TOPOLOGY AND ITS APPLICATIONS, 2010, 157 (02) : 456 - 465
  • [4] Notes on monotonically metacompact generalized ordered spaces
    Xu, Ai-Jun
    OPEN MATHEMATICS, 2015, 13 : 247 - 250
  • [5] EXISTENCE OF NORMAL METACOMPACT MOORE SPACES WHICH ARE NOT METRIZABLE
    TALL, FD
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1974, 26 (01): : 1 - 6
  • [6] PSEUDOCOMPACT METACOMPACT SPACES ARE COMPACT
    WATSON, WS
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 81 (01) : 151 - 152
  • [7] COMPACT METRIZABLE SPACES
    ALAS, OT
    ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI RENDICONTI-CLASSE DI SCIENZE FISICHE-MATEMATICHE & NATURALI, 1971, 50 (01): : 1 - &
  • [8] On (monotonically) metacompact subspaces of GO-spaces and related conclusions
    Peng, Liang-Xue
    Ma, Chun-Jie
    Wang, Li-Jun
    TOPOLOGY AND ITS APPLICATIONS, 2021, 295
  • [9] Monotonically star compact spaces
    Song, Yan-Kui
    TOPOLOGY AND ITS APPLICATIONS, 2015, 190 : 35 - 41
  • [10] RECONSTRUCTING COMPACT METRIZABLE SPACES
    Gartside, Paul
    Pitz, Max F.
    Suabedissen, Rolf
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (01) : 429 - 443
12345