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International Journal of Mathematics and Mathematical Sciences
Volume 29, Issue 2, Pages 85-98

Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces

Department of Mathematics, KLE Society's, G. H. College, Haveri 581110, Karnataka, India

Received 12 June 2000

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Andrijević (1986) introduced the class of semi-preopen sets in topological spaces. Since then many authors including Andrijević have studied this class of sets by defining their neighborhoods, separation axioms and functions. The purpose of this paper is to provide the new characterizations of semi-preopen and semi-preclosed sets by defining the concepts of semi-precontinuous mappings, semi-preopen mappings, semi-preclosed mappings, semi-preirresolute mappings, pre-semipreopen mappings, and pre-semi-preclosed mappings and study their characterizations in topological spaces. Recently, Dontchev (1995) has defined the concepts of generalized semi-preclosed (gsp-closed) sets and generalized semi-preopen (gsp-open) sets in topology. More recently, Cueva (2000) has defined the concepts like approximately irresolute, approximately semi-closed, contra-irresolute, contra-semiclosed, and perfectly contra-irresolute mappings using semi-generalized closed (sg-closed) sets and semi-generalized open (sg-open) sets due to Bhattacharyya and Lahiri (1987) in topology. In this paper for gsp-closed (resp., gsp-open) sets, we also introduce and study the concepts of approximately semi-preirresolute (ap-sp-irresolute) mappings, approximately semi-preclosed (ap-semi-preclosed) mappings. Also, we introduce the notions like contra-semi-preirresolute, contra-semi-preclosed, and perfectly contra-semi-preirresolute mappings to study the characterizations of semi-pre-T1/2 spaces defined by Dontchev (1995).