Keywords:z-supercontinuous function, F-supercontinuous function, Functionally regular space, Functionally Hausdorff space, F-completely regular space, F-quotient topology
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.
C. E. Aull, Notes on separation by continuous functions, Indag. Math. 31 (1969), 458–461.
C. E. Aull, Functionally regular spaces, Indag. Math. 38 (1976), 281–288.
N. Bourbaki, Elements of General Topology Part I, Hermann, Addison-Wesley, 1966.
H. Brandenburg, On spaces with G-basis, Arch. Math. 35 (1980), 544–547. http://dx.doi.org/10.1007/BF01235379
Z. Froli’k Generalization of compact and Lindel¨of spaces, Czechoslovak. Math. J. 13 (84) (1959), 172–217 (Russian).
N.C. Heldermann, Developability and some new regularity axioms, Can. J. Math. 33, no. 3 (1981), 641–663. http://dx.doi.org/10.4153/CJM-1981-051-9
E. Hewitt, On two problems of Urysohn, Ann. of Math. 47, no. 3 (1946), 503–509. http://dx.doi.org/10.2307/1969089
J. K. Kohli and R. Kumar, z-supercontinuous functions, Indian J. Pure Appl. Math. 33, no. 7 (2002), 1097–1108.
J. K. Kohli, D. Singh, R. Kumar and J. Aggarwal, Between continuity and set connectedness, preprint.
J. K. Kohli and D. Singh, D-supercontinuous functions, Indian J. Pure Appl. Math. 32, no. 2 (2001), 227–235.
J. K. Kohli and D. Singh, D-supercontinuous functions, Indian J. Pure Appl. Math. 34, no. 7 (2003), 1089–1100.
J. K. Kohli and D. Singh, Between compactness and quasicompactness, Acta Math. Hungar. 106, no. 4 (2005), 317–329. http://dx.doi.org/10.1007/s10474-005-0022-4
J. K. Kohli, D. Singh and J. Aggarwal, On certain weak variants of normality and factorizations of normality, preprint.
J. K. Kohli, D. Singh and J. Aggarwal, R-supercontinuous functions, communicated.
J. K. Kohli, D. Singh and R. Kumar, Some properties of strongly -continuous functions, Bull. Cal. Math. Soc. 100 (2008), 185–196.
N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly 67 (1960), 269. http://dx.doi.org/10.2307/2309695
J.Mack, Countable paracompactness and weak normality properties, Trans. Amer.Math. Soc. 148 (1970), 265–272. http://dx.doi.org/10.1090/S0002-9947-1970-0259856-3
B. M. Munshi and D. S. Bassan, Super-continuous mappings, Indian J. Pure Appl. Math. 13 (1982), 229–236.
T. Noiri, On -continuous functions, J. Korean Math. Soc. 16 (1980), 161–166.
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, Dâˆ—-supercontinuous functions, Bull. Cal. Math. Soc. 94, no. 2 (2002), 67–76.
D. Singh, cl-supercontinuous functions, Applied General Topology 8, no. 2 (2007), 293– 300.
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
W. T. Van Est and H. Freudenthal, Trennung durch stetige Funktionen in topologischen Raümen, Indagationes Math. 15 (1951), 359–368.
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.