Function Spaces and Strong Variants of Continuity

Applied General Topology

J.K. Kohli¹  D. Singh¹ 

[1] University of Delhi;

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 continuit;   

DOI  :  10.4995/agt.2008.1867

来源: DOAJ

【 摘 要 】

It is shown that if domain is a sum connected space and range is a T0-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.

【 授权许可】

Unknown