On almost cl-supercontinuous functions
Keywords:Change of topology, Cl-supercontinuity, Almost cl-supercontinuity, Continuity, Almost continuity, Perfect continuity, Almost perfect continuity, Slightly continuous
AbstractRecently the class of almost cl-supercontinuous functions between topological spaces has been studied in some detail. We conside rthis class of functions from the point of view of change(s) of topology. In particular, we conclude that this class of functions coincides with the usual class of continuous functions when the domain and codomain have been retopologized appropriately. Some of the consequences of this fact are considered in this paper.
D. Carnahan, Locally nearly compact spaces, Boll. U.M.I. 4 (1972), 146–153.
J. Dontchev, M. Ganster and I. Reilly, More on almost s-continuity, Indian J. Math. 41 (1999), 139-146.
J. Dugundji, Topology, Allyn and Bacon, Boston, Mass. 1966.
E. Ekici, Generalization of perfectly continuous, regular set connected and clopen functions, Acta Math. Hungar. 107, no. 3 (2005), 193–205. http://dx.doi.org/10.1007/s10474-005-0190-2
D. Gauld, M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, Continuity properties of functions, Coll. Math. Soc. Janos Bolyai 41 (1983), 311–322.
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 and D. Singh, Almost cl-supercontinuous functions, Appl. Gen. Topol. 10, no. 1, (2009), 1–12.
M. Mrsevic, I. L. Reilly and M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc. A 38 (1985), 40–54. http://dx.doi.org/10.1017/S1446788700022588
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.
I. L. Reilly and M. K. Vamanamurthy, On super-continuous mappings, Indian J. Pure Appl. Math. 14, no. 6 (1983), 767–772.
M. K. Singal and A. R. Singal, Almost continuous mappings, Yokohama Math. 3 (1968), 63–73.
D. Singh, cl-supercontinuous functions, Appl. Gen. Topol. 8, no. 2 (2007), 293–300.
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, Pacific J. Math. 50 (1974), 169–185. http://dx.doi.org/10.2140/pjm.1974.50.169
N. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78, no. 2 (1968), 103-118.
How to Cite
This journal is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.