δ-closure, θ-closure and generalized closed sets

Jiling Cao; Maximilian Ganster; Ivan L. Reilly; Markus Steiner

doi:10.4995/agt.2005.1964

Authors

Jiling Cao University of Auckland
Maximilian Ganster Graz University of Technology
Ivan L. Reilly University of Auckland
Markus Steiner Graz University of Technology

DOI:

https://doi.org/10.4995/agt.2005.1964

Keywords:

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

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.

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Author Biographies

Jiling Cao, University of Auckland

Department of Mathematics

Maximilian Ganster, Graz University of Technology

Department of Mathematics

Ivan L. Reilly, University of Auckland

Department of Mathematics

Markus Steiner, Graz University of Technology

Department of Mathematics

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