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 50 条

[1] Another note on the class of paracompact spaces whose product with every paracompact space is paracompact
Alster, K.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2012, 159 (06) : 1640 - 1644
[2] On the class of ω1-metrizable spaces whose product with every paracompact space is paracompact
Alster, K.
[J]. TOPOLOGY AND ITS APPLICATIONS, 2006, 153 (14) : 2508 - 2517
[3] ON THE PRODUCT OF A PERFECT PARACOMPACT SPACE AND A COUNTABLE PRODUCT OF SCATTERED PARACOMPACT SPACES
ALSTER, K
[J]. FUNDAMENTA MATHEMATICAE, 1987, 127 (03) : 241 - 246
[4] A NOTE ON PARACOMPACT SPACES
MICHAEL, E
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1953, 4 (05) : 831 - 838
[5] ON PRODUCT OF PARACOMPACT SPACES
MORITA, K
[J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1963, 39 (08): : 559 - &
[6] ON PRODUCT OF PARACOMPACT SPACES
TELGARSKY, R
[J]. BULLETIN DE L ACADEMIE POLONAISE DES SCIENCES-SERIE DES SCIENCES MATHEMATIQUES ASTRONOMIQUES ET PHYSIQUES, 1969, 17 (09): : 533 - +
[7] ON THE TOPOLOGICAL PRODUCT OF PARACOMPACT SPACES
SORGENFREY, RH
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1947, 53 (06) : 631 - 632
[8] NEW CLASS OF PARACOMPACT SPACES
WENNER, BR
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1972, 5 (AUG): : 356 - &
[9] ON A CLASS OF COUNTABLY PARACOMPACT SPACES
MACK, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 16 (03) : 467 - &
[10] A note on productively paracompact spaces
Junnila, Heikki
[J]. TOPOLOGY AND ITS APPLICATIONS, 2017, 230 : 550 - 561

← 1 2 3 4 5 →