On a class of sets between a-open sets and gδ-open sets

Jagadeesh B. Toranagatti


In this paper, a new class of sets called Da-open sets are introduced and investigated with the help of gδ-open and δ-closed sets. Relationships between this new class and other related classes of sets are established and as an application Da-continuous functions have been dened to study its properties in terms of Da-open sets.Finally, some properties of Da-closed graph and (D.a)-closed graphs are investigated.


a-open set,δ-open set,gδ-open,Da-open set,Da-closed set

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M. S. El-Naschie,On the uncertainty of Cantorian geometry and two slit experiment, Chaos, Solitons and Fractals, 9(3)(1998), 517-529.

E. D. Kalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on nite ordered sets, Topol. Appl. 36(1990), 1-17.

M. B. Smyth,Semi-Matrices, Closure Spaces and digital topology, Theore. Comput. Sci.5 (1995), 257-276.

M. S. El-Naschie,On the certication of heterotic strings, M theory and E* theory, Chaos Solitons Fractals, (2000), 23972408.

M. S. El-Naschie,The two-slit experement as the fundation of E-innity of high energy physics, Chaos, Solitons Fractals, 25 (2005), 509-514.

E. D. Khalimsky, R. Kopperman and P. R. Meyer,Computer graphics and connected topologies in nite ordered sets, Topology Appl.,36(1990), 117.

E. Kovalevsky and R. Kopperman,Some topology-based image processing algorithms,Ann NY. Acad. Sci., 728 (1994), 174-182.

E. Ekici,On a-open sets, A*-sets and decompositions of continuity and super-continuity, Annales Univ. Sci. Budapest, Rolando Eotvos,Sect.Math.,51(1)(2008), 39-51.

E. Ekici, Some generalizations of almost contra super continuity, Filomat Vol. 21, No. 2 (2007), 31-44

J. Dontchev, I. Arokiarani and K. Balachandran, On generalized δ-closed sets and almost weakly Hausdroff spaces, Questions and Answersin Gen.Topology18(1) (2000), 17-30.

N. Levine,Generalized closed sets in topology, Rent. Circ. Mat. Palermo,19(1970), 89-96.

N.V. Veliko, H-closed topological Spaces, Amer. Math.Soc. Transl., 78(1968),103-118.

DOI: http://dx.doi.org/10.23755/rm.v39i0.535


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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.