Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces
Summary: \textit{D. Andrijević} [Mat. Vesn. 38, 24-32 (1986; Zbl 0604.54002)] 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, \textit{J. Dontchev} [Mem. Fac. Sci., Kochi{} Univ., Ser. A 16, 35-48 (1995; Zbl 0833.54001)] has defined the concepts of generalized semi-preclosed (gsp-closed) sets and generalized semi-preopen (gsp-open) sets in topology. More recently, \textit{M. Caldas Cueva} [Int. J. Math. Math. Sci. 23, No. 4, 253-259 (2000; Zbl 0982.54018)] 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 \textit{P. Bhattacharyya} and \textit{B. K. Lahiri} [Indian J. Math. 29, No. 3, 375-382 (1987; Zbl 0687.54002)] 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-\(T_{1/2}\) spaces defined by Dontchev [loc. cit.].
scientific article; zbMATH DE number 1780321