Function Spaces and Strong Variants of Continuity | Zendy

J. K. Kohli | Zendy; D. Singh | Zendy

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Function Spaces and Strong Variants of Continuity

Author(s) -

J. K. Kohli,

D. Singh

Publication year - 2008

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2008.1867

Subject(s) - mathematics , pointwise , hausdorff space , pointwise convergence , space (punctuation) , closed set , function space , pure mathematics , continuous function (set theory) , function (biology) , normal space , uniform limit theorem , continuous functions on a compact hausdorff space , topological space , range (aeronautics) , set (abstract data type) , topology (electrical circuits) , mathematical analysis , combinatorics , topological vector space , network topology , computer science , materials science , evolutionary biology , composite material , biology , operating system , programming language

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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