When is an Almost Locally Compact Space Supercomplete?

Chinese Quarterly Journal of Mathematics >

2016 , Vol. 31 >Issue 4: 430 - 434

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2016.04.012

When is an Almost Locally Compact Space Supercomplete?

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School of Mathematics and Statistics,Minnan Normal University

LI Xiao-ting(1990-), female, native of Huizhou, Guangdong, M.S.D., engages in general topology; LIN Fu-cai(1979-), male, native of Quanzhou, Fujian, an associate professor of Minnan Normal University, Ph.D., engages in general topology.

Received date: 2015-03-27

Online published: 2020-11-03

Supported by

Supported by the National Natural Science Foundation of China(11201414,11571158,11171162)； Supported by the Natural Science Foundation of Fujian Province(2012J05013)； Supported by the Training Programme Foundation for Excellent Youth Researching Talents of Fujian’s Universities(JA13190)；

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Abstract

It is proved in this paper that(1) the topological sum of a family of supercomplete spaces is supercomplete;(2) if X is a metacompact and almost locally compact space then X is supercomplete. Moreover, some questions on supercomplete spaces are posed in the paper.

Key words： supercomplete spaces; sums of topological spaces; almost locally compact; metacompact spaces

Cite this article

LI Xiao-ting, LIN Fu-cai . When is an Almost Locally Compact Space Supercomplete?[J]. Chinese Quarterly Journal of Mathematics, 2016 , 31(4) : 430 -434 . DOI: 10.13371/j.cnki.chin.q.j.m.2016.04.012

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