A note on the class of paracompact spaces whose product with every paracompact space is paracompact

被引：8

作者：

Alster, K. ^{[1
,2
]}

机构：

[1] Cardinal Stefan Wyszynski Univ Warsaw, Sch Sci, Fac Math & Sci, Warsaw, Poland

[2] Polish Acad Sci, Inst Math, Warsaw, Poland

来源：

TOPOLOGY AND ITS APPLICATIONS | 2009年 / 156卷 / 07期

关键词：

Paracompact; Product spaces; LINDELOF;

D O I：

10.1016/j.topol.2008.12.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that if X is a paracompact space which has a neighborhood assignment x -> H(x) Such that for each y is an element of X the closure of the set (x is an element of X: y is an element of H(x)) is compact then the products T x X, for every paracompact space T, and X(omega) are paracompact. The first result answers a problem of H. Junnila. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：1345 / 1347

页数：3

共 13 条

[1] Base-paracompact spaces
Porter, JE
TOPOLOGY AND ITS APPLICATIONS, 2003, 128 (2-3) : 145 - 156
[2] β1-paracompact spaces
AlJarrah, Heyam Hussain
JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (04): : 1728 - 1734
[3] The gap between the dimensions of countably paracompact spaces
Charalambous, Michael G.
TOPOLOGY AND ITS APPLICATIONS, 2008, 155 (17-18) : 2216 - 2220
[4] PRODUCTS OF BASE-κ-PARACOMPACT SPACES AND COMPACT SPACES
Mou, Lei
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2011, 84 (03) : 387 - 392
[5] Σ-products of paracompact C-scattered spaces
Tanaka, H
Yajima, Y
TOPOLOGY AND ITS APPLICATIONS, 2002, 124 (01) : 39 - 46
[6] Some remarks on S-paracompact spaces
P. -Y. Li
Y. -K. Song
Acta Mathematica Hungarica, 2008, 118 : 345 - 355
[7] Σ-products of paracompact DC-LIKE spaces
Hanaoka, J
Tanaka, H
TOPOLOGY PROCEEDINGS, VOL 26, NO 1, 2001-2002, 2002, 26 (01): : 199 - 212
[8] Hereditarily paracompact and compact monotonically normal spaces
Rudin, ME
TOPOLOGY AND ITS APPLICATIONS, 2001, 111 (1-2) : 179 - 189
[9] There is a paracompact Q-set space in ZFC
Balogh, ZT
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (06) : 1827 - 1833
[10] Locally compact perfectly normal spaces may all be paracompact
Larson, Paul B.
Tall, Franklin D.
FUNDAMENTA MATHEMATICAE, 2010, 210 (03) : 285 - 300

← 1 2 →