F-supercontinuous functions

Authors

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

DOI:

https://doi.org/10.4995/agt.2009.1788

Keywords:

z-supercontinuous function, F-supercontinuous function, Functionally regular space, Functionally Hausdorff space, F-completely regular space, F-quotient topology

Abstract

A strong variant of continuity called ‘F-supercontinuity’ is introduced. The class of F-supercontinuous functions strictly contains the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33 (7) (2002), 1097–1108) which in turn properly contains the class of cl-supercontinuous functions ( clopen maps) (Appl. Gen. Topology 8 (2) (2007), 293–300; Indian J. Pure Appl. Math. 14 (6) (1983), 762–772). Further, the class of F-supercontinuous functions is properly contained in the class of R-supercontinuous functions which in turn is strictly contained in the class of continuous functions. Basic properties of F-supercontinuous functions are studied and their place in the hierarchy of strong variants of continuity, which already exist in the mathematical literature, is elaborated. If either domain or range is a functionally regular space (Indagationes Math. 15 (1951), 359–368; 38 (1976), 281–288), then the notions of continuity, F-supercontinuity and R-supercontinuity coincide.

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Author Biographies

J.K. Kohli, University of Delhi

Department of Mathematics

D. Singh, University of Delhi

Department of Mathematics

Jeetendra Aggarwal, University of Delhi

Department of Mathematics

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How to Cite

[1]
J. Kohli, D. Singh, and J. Aggarwal, “F-supercontinuous functions”, Appl. Gen. Topol., vol. 10, no. 1, pp. 69–83, Apr. 2009.

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Section

Regular Articles