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.
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页码：33 / 38
页数：6
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