Keywords:Clopen continuous function, Supercontinuous function, Perfectly continuous function, Strongly continuous function, Zero-dimensional space, Ultra-Hausdorff space
Basic properties of cl-supercontinuity, a strong variant of continuity, due to Reilly and Vamanamurthy [Indian J. Pure Appl. Math., 14 (1983), 767–772], who call such maps clopen continuous, are studied. Sufficient conditions on domain or range for a continuous function to be cl-supercontinuous are observed. Direct and inverse transfer of certain topological properties under cl-supercontinuous functions are studied and existence or nonexistence of certain cl-supercontinuous function with specified domain or range is outlined.
R. C. Jain, The role of regularly open sets in general topology, Ph.D. thesis, Meerut Univ., Institute of Advanced Studies, Meerut, India (1980).
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
J. K. Kohli and R. Kumar, Z-supercontinuous functions, Indian J. Pure Appl. Math. 33 (7) (2002), 1097–1108.
J. K. Kohli and D. Singh, D-supercontinuous functions, Indian J. Pure Appl. Math. 32 (2) (2001), 227–235.
J. K. Kohli and D. Singh, Dδ-supercontinuous functions, Indian J. Pure Appl. Math. 34 (7) (2003), 1089–1100.
J. K. Kohli and D. Singh, Function spaces and strong variants of continuity, Applied Gen. Top.
J. K. Kohli, D. Singh and Rajesh Kumar, Some properties of strongly θ-continuous functions, Communicated.
N. Levine, Strongly continuity in topological spaces, Amer. Math. Monthly 67 (1960), 269. http://dx.doi.org/10.2307/2309695
B. M. Munshi and D.S. Bassan, Super-continuous mappings, Indian J. Pure Appl. Math. 13 (1982), 229–236.
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 (3) (1984), 241–250.
I. L. Reilly and M. K. Vamanamurthy, On super-continuous mappings, Indian J. Pure. Appl. Math. 14 (6) (1983), 767–772.
D. Singh, Dâˆ—-supercontinuous functions, Bull. Cal. Math. Soc. 94 (2) (2002), 67–76.
A. Sostak, On a class of topological spaces containing all bicompact and connected spaces, General Topology and its Relation to Modern Analysis and Algebra IV: Proceedings of the 4th Prague Topological Symposium, (1976), Part B, 445–451.
R. Staum, The algebra of bounded continuous functions into a nonarchimedean field, Pac. J. Math. 50 (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
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.