Function Spaces and Strong Variants of Continuity

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

References

R. F. Brown, Ten topologies for X×Y , Quarterly J. Math. (Oxford) 14 (1963), 303–319. http://dx.doi.org/10.1093/qmath/14.1.303

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. http://dx.doi.org/10.1002/mana.19780820113

N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly 67 (1960), 269. http://dx.doi.org/10.2307/2309695

E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 7 (1951), 152–182. http://dx.doi.org/10.1090/S0002-9947-1951-0042109-4

S. A. Naimpally, On strongly continuous functions, Amer. Math. Monthly 74 (1967), 166–168. http://dx.doi.org/10.2307/2315609

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. http://dx.doi.org/10.2140/pjm.1974.50.169

L. A. Steen and J. A. Seeback, Jr., Counter Examples in Topology, Springer Verlag, New York, 1978. http://dx.doi.org/10.1007/978-1-4612-6290-9

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How to Cite

[1]
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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