Function Spaces and Strong Variants of Continuity


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



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


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


R. F. Brown, Ten topologies for X×Y , Quarterly J. Math. (Oxford) 14 (1963), 303–319.

S. P. Franklin, Natural covers, Composito Mathematica 21 (1969), 253–261.

J. L. Kelly, General Topology, D. Van Nostand Company, Inc., 1955.

J. K. Kohli, A class of spaces containing all connected and all locally connected spaces, Math. Nachricten 82 (1978), 121–129.

N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly 67 (1960), 269.

E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 7 (1951), 152–182.

S. A. Naimpally, On strongly continuous functions, Amer. Math. Monthly 74 (1967), 166–168.

T. Noiri, Supercontinuity and some strong forms of continuity, Indian J. Pure. Appl. Math. 15, no. 3 (1984), 241–250.

I. L. Reilly and M. K. Vamanamurthy, On super-continuous mappings, Indian J. Pure. Appl. Math. 14, no. 6 (1983), 767–772.

D. Singh, cl-supercontinuous functions, Applied Gen. Top. (accepted).

R. Staum, The Algebra of bounded continuous functions into a nonarchimedean field, Pac. J. Math. 50, no. 1 (1974), 169–185.

L. A. Steen and J. A. Seeback, Jr., Counter Examples in Topology, Springer Verlag, New York, 1978.


How to Cite

J. Kohli and D. Singh, “Function Spaces and Strong Variants of Continuity”, Appl. Gen. Topol., vol. 9, no. 1, pp. 33–38, Apr. 2008.



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