Between continuity and set connectedness

Authors

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

DOI:

https://doi.org/10.4995/agt.2010.1727

Keywords:

Almost continuous function, D-continuous function, z-continuous function, Quasi θ-continuous function, Faintly continuous function, Functionally Hausdorff space, Zero set

Abstract

Two new weak variants of continuity called 'R-continuity'and 'F-continuity' are introduced. Their basic properties are studied and their place in the hierarchy of weak variants of continuity, that already exist in the literature, is elaborated. The class of R-continuous functions properly contains the class of continuous functions and is strictly contained in each of the three classes of (1) faintly continu-ous functions studied by Long and Herrignton (Kyungpook Math. J.22(1982), 7-14); (2) D-continuous functions introduced by Kohli (Bull.Cal. Math. Soc. 84 (1992), 39-46), and (3) F-continuous functions which in turn are strictly contained in the class of z-continuous functions studied by Singal and Niemse (Math. Student 66 (1997), 193-210).So the class of R-continuous functions is also properly contained in each of the classes of D∗-continuous functions, D-continuous function and set connected functions.

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Author Biographies

J.K. Kohli, University of Delhi

Department of Mathematics, Hindu College, University of Delhi, Delhi 110 007, India

D. Singh, University of Delhi

Department of Mathematics, Sri Aurobindo College, University of Delhi-South Campus, Delhi 110 017, India

Rajesh Kumar, University of Delhi

Department of Mathematics

Jeetendra Aggarwal, University of Delhi

Department of Mathematics, University of Delhi, Delhi 110 007, India

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How to Cite

[1]
J. Kohli, D. Singh, R. Kumar, and J. Aggarwal, “Between continuity and set connectedness”, Appl. Gen. Topol., vol. 11, no. 1, pp. 43–55, Apr. 2010.

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Regular Articles