×

On \(\delta\)-perfectly continuous functions. (English) Zbl 1253.54016

Summary: Recently the class of \(\delta\)-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 \(\delta\)-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.

MSC:

54C08 Weak and generalized continuity
54C60 Set-valued maps in general topology
54C05 Continuous maps
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] P. Alexandroff, Discrete Räume, Mat. Sb. 2 (1937), 501-518.;
[2] D. Carnahan, Locally nearly compact spaces, Boll. Un. Mat. Ital. 4 (1972), 146-153.; · Zbl 0257.54020
[3] J. Dontchev, M. Ganster, I. L. Reilly, More on almost s-continuity, Indian J. Math. 41 (1999), 139-146.; · Zbl 1033.54502
[4] J. Dontchev, Contra-continuous functions and strongly s-closed spaces, Internat. J. Math. Math. Sci. 19(2) (1996), 303-310.; · Zbl 0840.54015
[5] J. Dugundji, Topology, Allyn and Bacon, Boston, Mass. 1966.;
[6] L. L. Herrington, Properties of nearly compact spaces, Proc. Amer. Math. Soc. 45 (1974), 431-436.; · Zbl 0313.54009
[7] J. K. Kohli, D. Singh, δ-perfectly continuous functions, Demonstratio Math. 42(1) (2009), 221-231.; · Zbl 1167.54303
[8] J. K. Kohli, D. Singh, C. P. Arya, Perfectly continuous functions, Stud. Cerc. Mat. 18 (2008), 99-110.; · Zbl 1199.54078
[9] M. Mrsevic, I. L. Reilly, M. K. Vamanamurthy, On semi-regularization topologies, J. Austral. Math. Soc. A 38 (1985), 40-54.; · Zbl 0561.54002
[10] B. M. Munshi, D. S. Bassan, Super-continuous mappings, Indian J. Pure Appl. Math. 13 (1982), 229-236.; · Zbl 0483.54007
[11] T. Noiri, On δ-continuous functions, J. Korean Math. Soc. 16 (1980), 161-166.; · Zbl 0435.54010
[12] T. Noiri, Supercontinuity and some strong forms of continuity, Indian J. Pure. Appl. Math. 15(3) (1984), 241-250.; · Zbl 0546.54016
[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.;
[14] R. Staum, The algebra of bounded continuous functions into a nonarchimedean field, Pacific J. Math. 50 (1974), 169-185.; · Zbl 0296.46052
[15] N. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78(2) (1968), 103-118.;
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.