Abstract
Recently the class of δ-perfectly continuous functions between topological spaces has been introduced and studied in some detail. In this paper we consider this class of functions from the point of view of change of topology. In particular, we demonstrate that the concept of δ-perfect continuity coincides with the notion of perfect continuity when the codomain of the function under consideration has been retopologized appropriately. This paper considers some of the consequences of this fact.
References
[1] P. Alexandroff, Discrete Räume, Mat. Sb. 2 (1937), 501–518.Search in Google Scholar
[2] D. Carnahan, Locally nearly compact spaces, Boll. Un. Mat. Ital. 4 (1972), 146–153.Search in Google Scholar
[3] J. Dontchev, M. Ganster, I. L. Reilly, More on almost s-continuity, Indian J. Math. 41 (1999), 139–146.Search in Google Scholar
[4] J. Dontchev, Contra-continuous functions and strongly s-closed spaces, Internat. J. Math. Math. Sci. 19(2) (1996), 303–310.10.1155/S0161171296000427Search in Google Scholar
[5] J. Dugundji, Topology, Allyn and Bacon, Boston, Mass. 1966.Search in Google Scholar
[6] L. L. Herrington, Properties of nearly compact spaces, Proc. Amer. Math. Soc. 45 (1974), 431–436.10.1090/S0002-9939-1974-0346748-3Search in Google Scholar
[7] J. K. Kohli, D. Singh, δ-perfectly continuous functions, Demonstratio Math. 42(1) (2009), 221–231.10.1515/dema-2013-0143Search in Google Scholar
[8] J. K. Kohli, D. Singh, C. P. Arya, Perfectly continuous functions, Stud. Cerc. Mat. 18 (2008), 99–110.Search in Google Scholar
[9] M. Mrsevic, I. L. Reilly, M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc. A 38 (1985), 40–54.10.1017/S1446788700022588Search in Google Scholar
[10] B. M. Munshi, D. S. Bassan, Super-continuous mappings, Indian J. Pure Appl. Math. 13 (1982), 229–236.Search in Google Scholar
[11] T. Noiri, On δ-continuous functions, J. Korean Math. Soc. 16 (1980), 161–166.Search in Google Scholar
[12] T. Noiri, Supercontinuity and some strong forms of continuity, Indian J. Pure. Appl. Math. 15(3) (1984), 241–250.Search in Google Scholar
[13] 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.Search in Google Scholar
[14] R. Staum, The algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math. 50 (1974), 169–185.10.2140/pjm.1974.50.169Search in Google Scholar
[15] N. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78(2) (1968), 103–118.10.1090/trans2/078/05Search in Google Scholar
© 2012 S. Bayhan et al., published by De Gruyter Open
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.
