函数空间中的AP性质

数学季刊 ›› 2012, Vol. 27 ›› Issue (3): 447-451.

函数空间中的AP性质

Department of Mathematics, Taizhou Teacher’s College; Department of Mathematics, Nanjing University

收稿日期:2011-05-30 出版日期:2012-09-30 发布日期:2023-03-24
作者简介:SHEN Rong-xin(1981-), male, native of Taizhou, Jiangsu, an associate professor of Taizhou Teacher’s College, Ph.D., engages in general topology.
基金资助:
Supported by the NNSF of China(10971185); Supported by the China Postdoctoral Science Foundation Funded Project(20090461093,201003571)； Supported by the Jiangsu Planned Projects for Postdoctoral Research Funds(0902064C)；Supported by the Taizhou Teachers’ College Research Funds

On AP-property of Function Spaces

Department of Mathematics, Taizhou Teacher’s College; Department of Mathematics, Nanjing University

Received:2011-05-30 Online:2012-09-30 Published:2023-03-24
About author:SHEN Rong-xin(1981-), male, native of Taizhou, Jiangsu, an associate professor of Taizhou Teacher’s College, Ph.D., engages in general topology.
Supported by:
Supported by the NNSF of China(10971185); Supported by the China Postdoctoral Science Foundation Funded Project(20090461093,201003571)； Supported by the Jiangsu Planned Projects for Postdoctoral Research Funds(0902064C)；Supported by the Taizhou Teachers’ College Research Funds

摘要/Abstract

摘要： In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if C_α(X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if C_α(X) is an AP-space which has countable tightness, then C_α(X) is discretely generated.

关键词: AP-spaces, function spaces, Hurewics spaces, discretely generated spaces

Abstract:

In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if Cα(X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if Cα(X) is an AP-space which has countable tightness, then Cα(X) is discretely generated.

Key words: AP-spaces, function spaces, Hurewics spaces, discretely generated spaces

中图分类号:

O189.11

沈荣鑫. 函数空间中的AP性质[J]. 数学季刊, 2012, 27(3): 447-451.

SHEN Rong-xin. On AP-property of Function Spaces [J]. Chinese Quarterly Journal of Mathematics, 2012, 27(3): 447-451.