Function Spaces and Strong Variants of Continuity

J.K. Kohli; D. Singh

doi:10.4995/agt.2008.1867

Authors

J.K. Kohli University of Delhi
D. Singh University of Delhi

DOI:

https://doi.org/10.4995/agt.2008.1867

Keywords:

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

Abstract

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.

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Author Biographies

J.K. Kohli, University of Delhi

Department of Mathematics, Hindu College

D. Singh, University of Delhi

Department of Mathematics, Sri Aurobindo College

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