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Kohli, J. K.; Tyagi, B. K.; Singh, D.; Aggarwal, Jeetendra

\(R_\delta\)-supercontinuous functions. (English) Zbl 1300.54022

Demonstr. Math. 47, No. 2, 433-448 (2014).
Summary: A new class of functions called ‘\(R_\delta\)-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of \(R_\delta\)-supercontinuous functions properly contains the class of \(R_{z}\)-supercontinuous functions which in its turn properly contains the class of \(R_{cl}\)-supercontinuous functions and so includes all \(R_{cl}\)-supercontinuous (\(\equiv\)clopen continuous) functions and is properly contained in the class of \(R\)-supercontinuous functions.

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MSC:

54C08 Weak and generalized continuity
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D10 Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)

Keywords:

\(z\)-supercontinuous function; \(F\)-supercontinuous function; \(cl\)-supercontinuous function; \(R_z\)-supercontinuous function; \(R\)-supercontinuous function; \(r_\delta\)-open (\(r_\delta\)-closed)set; \(\delta\)-embedded; weakly Hausdorff space (\(\equiv \delta T_1\)-space); \(\delta T_0\)-space
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\textit{J. K. Kohli} et al., Demonstr. Math. 47, No. 2, 433--448 (2014; Zbl 1300.54022)
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References:

[1] F. Beckhoff, Topologies on the spaces of ideals of a Banach algebra, Studia Math. 115 (1995), 189-205.; · Zbl 0836.46038
[2] F. Beckhoff, Topologies on the ideal space of a Banach algebra and spectral synthesis, Proc. Amer. Math. Soc. 125 (1997), 2859-2866.; · Zbl 0883.46032
[3] A. S. Davis, Indexed system of neighbourhoods for general topological spaces, Amer.Math. Monthly 68 (1961), 886-893.;
[4] E. Ekici, Generalization of perfectly continuous, regular set-connected and clopen functions, Acta Math. Hungar. 107(3) (2005), 193-206.; · Zbl 1081.54011
[5] A. M. Gleason, Universal locally connected refinements, Illinois J. Math. 7 (1963), 521-531.; · Zbl 0117.16101
[6] J. K. Kohli, A class of mappings containing all continuous and all semiconnected mappings, Proc. Amer. Math. Soc. 72(1) (1978), 175-181.; · Zbl 0408.54003
[7] J. K. Kohli, A framework including the theories of continuous and certain noncontinuous functions, Note Mat. 10(1) (1990), 37-45.; · Zbl 0780.54008
[8] J. K. Kohli, A unified approach to continuous and certain non-continuous functions, J. Aust. Math. Soc. 48(3) (1990), 347-358.; · Zbl 0702.54010
[9] J. K. Kohli, A unified approach to continuous and certain non-continuous functions II , Bull. Austral. Math. Soc. 41(1) (1990), 57-74.; · Zbl 0705.54010
[10] J. K. Kohli, Change of topology, characterizations and product theorems for semilocally P-spaces, Houston J. Math. 17(3) (1991), 335-350.; · Zbl 0781.54007
[11] J. K. Kohli, R. Kumar, z-supercontinuous functions, Indian J. Pure Appl. Math. 33(7) (2002), 1097-1108.; · Zbl 1010.54012
[12] J. K. Kohli, D. Singh, D_-supercontinuous functions, Indian J. Pure Appl. Math. 34(7) (2003), 1089-1100.; · Zbl 1036.54003
[13] J. K. Kohli, D. Singh, Almost cl-supercontinuous functions, Appl. Gen. Topol. 10(1) (2009), 1-12.; · Zbl 1190.54008
[14] J. K. Kohli, D. Singh,_-perfectly continuous functions, Demonstratio Math. 42(1) (2009), 221-231.; · Zbl 1167.54303
[15] J. K. Kohli, D. Singh, Separation axioms between regularity and R0-spaces, (preprint).;
[16] J. K. Kohli, D. Singh, J. Aggarwal, F-supercontinuous functions, Appl. Gen. Topol. 10(1) (2009), 69-83.; · Zbl 1189.54013
[17] J. K. Kohli, D. Singh, J. Aggarwal, R-supercontinuous functions, Demonstratio Math. 43(3) (2010), 703-723.; · Zbl 1217.54016
[18] J. K. Kohli, D. Singh, J. Aggarwal, R_-supercontinuous functions, (preprint).; · Zbl 1189.54013
[19] J. K. Kohli, D. Singh, C. P. Arya, Perfectly continuous functions, Stud. Cercet. Stiint.Ser. Mat. Univ. Bacau 18 (2008), 99-110.; · Zbl 1199.54078
[20] J. K. Kohli, D. Singh, R. Kumar, Some properties of strongly_-continuous functions, Bull. Calcutta Math. Soc. 100 (2008), 185-196.; · Zbl 1387.54002
[21] J. Mack, Countable paracompactness and weak normality properties, Trans. Amer.Math. Soc. 148 (1970), 265-0272.; · Zbl 0209.26904
[22] N. Levine, Strong continuity in topological spaces, Amer. Math. Monthly 67 (1960), 269.; · Zbl 0156.43305
[23] B. M. Munshi, D. S. Bassan, Super-continuous mappings, Indian J. Pure Appl. Math. 13 (1982), 229-236.; · Zbl 0483.54007
[24] T. Noiri, On_-continuous functions, J. Korean Math. Soc. 16 (1980), 161-166.; · Zbl 0435.54010
[25] T. Noiri, Supercontinuity and some strong forms of continuity, Indian J. Pure. Appl.Math. 15(3) (1984), 241-250.; · Zbl 0546.54016
[26] I. L. Reilly, M. K. Vamanamurthy, On super-continuous mappings, Indian J. Pure.Appl. Math. 14(6) (1983), 767-772.; · Zbl 0509.54007
[27] N. A. Shanin, On separation in topological spaces, Dokl. Akad. Nauk 38(1943), 110-113.; · Zbl 0061.39607
[28] D. Singh, D_-supercontinuous functions, Bull. Calcutta Math. Soc. 94(2) (2002), 67-76.; · Zbl 1012.54016
[29] D. Singh, cl-supercontinuous functions, Appl. Gen. Topol. 8(2) (2007), 293-300.; · Zbl 1151.54012
[30] D. Singh, B. K. Tyagi, J. Aggarwal, J. K. Kohli, Rz-supercontinuous functions, Math.Bohem. (to appear).; · Zbl 1349.54043
[31] D. W. B. Somerset, Ideal spaces of Banach algebras, Proc. London Math. Soc. 78(3) (1999), 369-400.; · Zbl 1027.46058
[32] T. Soundararajan, Weakly Hausdorff spaces and cardinality of spaces, General Topology and its relations to Modern Analysis and Algebra, Proceedings Kanpur Topology Conference 1968, Academia, Prague 1971, 301-306.;
[33] L. A. Steen, J. A. Seeback, Jr., Counter Examples in Topology, Springer Verlag, New York, 1978.;
[34] B. K. Tyagi, J. K. Kohli, D. Singh, Rcl-supercontinuous functions, Demonstratio Math. 46(1) (2013), 229-244.; · Zbl 1272.54015
[35] R. Vaidyanathswamy, Treatise on Set Topology, Chelsea Publishing Company, New York, 1960.;
[36] N. V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (1968), 103-118.;
[37] C. T. Yang, On paracompact spaces, Proc. Amer. Math. Soc. 5(2) (1954), 185-194.;
[38] G. S. Young, Introduction of local connectivity by change of topology, Amer. J. Math. 68 (1946), 479-494.; · Zbl 0060.40204
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.