Function Spaces and Strong Variants of Continuity

被引：5

作者：

Kohli, J. K. ^{[1
]}

Singh, D. ^{[2
]}

机构：

[1] Univ Delhi, Hindu Coll, Dept Math, Delhi 110007, India

[2] Univ Delhi, Sri Aurobindo Coll, Dept Math, South Campus, Delhi 110007, India

来源：

APPLIED GENERAL TOPOLOGY | 2008年 / 9卷 / 01期

关键词：

Strongly continuous function; perfectly continuous function; cl-supercontinuous function; sum connected spaces; k-space; topology of point wise convergence; topology of uniform convergence on compacta; compact open topology; equicontinuity; even continuity;

D O I：

10.4995/agt.2008.1867

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that if domain is a sum connected space and range is a To-space, then the notions of strong continuity, perfect continuity and cl-supercontinuity coincide. Further, it is proved that if X is a sum connected space and Y is Hausdorff, then the set of all strongly continuous (perfectly continuous, cl-supercontinuous) functions is closed in Y-X in the topology of pointwise convergence. The results obtained in the process strengthen and extend certain results of Levine and Naimpally.

引用

页码：33 / 38

页数：6

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