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).
