δ-closure, θ-closure and generalized closed sets

Jiling Cao

New Zealand

University of Auckland

Department of Mathematics

Maximilian Ganster

Austria

Graz University of Technology

Department of Mathematics

Ivan L. Reilly

New Zealand

University of Auckland

Department of Mathematics

Markus Steiner

Austria

Graz University of Technology

Department of Mathematics
|

Accepted: 2013-11-26

|
DOI: https://doi.org/10.4995/agt.2005.1964
Funding Data

Downloads

Keywords:

δ-closed, θ-closed, qr-closed, separation properties

Supporting agencies:

This research was not funded

Abstract:

We study some new classes of generalized closed sets (in the sense of N. Levine) in a topological space via the associated δ-closure and θ-closure. The relationships among these new classes and existing classes of generalized closed sets are investigated. In the last section we provide an extensive and more or less complete survey on separation axioms characterized via singletons.

Show more Show less

References:

J. Cao, M. Ganster and I. Reilly, On generalized closed sets, Topology & Appl. 123 (2002), 37-46. http://dx.doi.org/10.1016/S0166-8641(01)00167-5

J. Cao, M. Ganster and I. Reilly, Submaximality, extremal disconnectedness and generalized closed sets, Houston J. Math. 24 (1998), 681-688.

J. Cao, S. Greenwood and I.Reilly, Generalized closed sets: a unified approach, Applied General Topology 2 (2001), 179-189.

K. Dlaska and M. Ganster, S-sets and co-S-closed topologies, Indian J. Pure Appl. Math. 23 (1992), 731-737.

J. Dontchev, I. Arokiarani and K. Balachandran, On generalized δ-closed sets and almost weakly Hausdorff spaces, Q & A in General Topology 18 (2000), 17-30.

J. Dontchev and M. Ganster, On δ-generalized closed sets and T3/4 spaces, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 17 (1996), 15-31.

J. Dontchev and H. Maki, On θ-generalized closed sets, Internat. J. Math. & Math. Sci. 22 (1999), 239-249. http://dx.doi.org/10.1155/S0161171299222399

W. Dunham, T1/2-spaces, Kyungpook Math. J. 17 (1977), 161-169.

D. Jankovic, On some separation axioms and θ-closure, Mat. Vesnik 32 (4) (1980), 439-449.

D. Jankovic and I. Reilly, On semi-separation properties, Indian J. Pure Appl. Math. 16 (1985), 957-964.

N. Levine, Generalized closed sets in topological spaces, Rend. Circ. Mat. Palermo 19 (1970), 89-96. http://dx.doi.org/10.1007/BF02843888

S. N. Maheshwari and U. Tapi, Feebly T1-spaces, An. Univ. Timisoara Ser. Stiint. Mat 16 (1978), no.2, 173-177.

T. Soundararajan, Weakly Hausdorff spaces and the cardinality of topological spaces, General Topology and its Relations to Modern Analysis and Algebra III, Proc. Conf. Kanpur 1968, Academia, Prague (1971), 301-306.

M. Steiner, Verallgemeinerte abgeschlossene Mengen in topologischen Räumen, Master Thesis, Graz University of Technology, 2003.

N.V. Velicko, H-closed topological spaces, Amer. Math. Soc. Transl. 78 (2) (1968), 103-118.

Show more Show less