基-中紧空间

数学季刊 ›› 2010, Vol. 25 ›› Issue (3): 430-435.

基-中紧空间

1. Department of Applied Mathematics, Chengdu University of Technology2. Department of Mathematics, Leshan Teachers College

收稿日期:2008-01-05 出版日期:2010-09-30 发布日期:2023-05-29
作者简介:CAO Jin-wen(1956- ), male, native of Zizhong, Sichuan, a professor of Chengdu University of Technology, Ph.D., engages in topology and functional analysis topology.
基金资助:
Supported by the Department of Education Sichuan Province Foundation for Science Research(2006C041)；

Base-mesocompact Spaces

1. Department of Applied Mathematics, Chengdu University of Technology2. Department of Mathematics, Leshan Teachers College

Received:2008-01-05 Online:2010-09-30 Published:2023-05-29
About author:CAO Jin-wen(1956- ), male, native of Zizhong, Sichuan, a professor of Chengdu University of Technology, Ph.D., engages in topology and functional analysis topology.
Supported by:
Supported by the Department of Education Sichuan Province Foundation for Science Research(2006C041)；

摘要/Abstract

摘要： In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained: (1) Let X be base-mesocompact and X’ an F σ subset of X. If X is normal, then X’ is base-mesocompact relative to X. (2) Let f: X → Y be a base-mesocompact mapping, ω(X) be a regular cardinality of X and ω(X) ≥ω(Y). If Y is base-mesocompact and regular, then X is base-mesocompact. (3) Let f: X → Y be a closed lindel of mapping with regular domain and regular range. If Y is base-mesocompact, then X is base-mesocompact. (4) Let X be base-mesocompact. If Y is locally compact and base-esocompact, then X × Y is base-mesocompact.

关键词: base-mesocompact, base-paracompact mapping, base-mesocompact mapping;
closed lindelof mapping

Abstract: In this paper the notation of base-mesocompactness is introduced and the following results are mainly obtained: (1) Let X be base-mesocompact and X’ an F σ subset of X. If X is normal, then X’ is base-mesocompact relative to X. (2) Let f: X → Y be a base-mesocompact mapping, ω(X) be a regular cardinality of X and ω(X) ≥ω(Y). If Y is base-mesocompact and regular, then X is base-mesocompact. (3) Let f: X → Y be a closed lindel of mapping with regular domain and regular range. If Y is base-mesocompact, then X is base-mesocompact. (4) Let X be base-mesocompact. If Y is locally compact and base-esocompact, then X × Y is base-mesocompact.

Key words: base-mesocompact, base-paracompact mapping, base-mesocompact mapping;
closed lindelof mapping

中图分类号:

O189.11

曹金文, 宋际平, 刘徽. 基-中紧空间[J]. 数学季刊, 2010, 25(3): 430-435.

CAO Jin-wen, SONG Ji-ping, LIU Hui. Base-mesocompact Spaces[J]. Chinese Quarterly Journal of Mathematics, 2010, 25(3): 430-435.

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