Andrijević (1986) introduced the class of semi-preopen setsin topological spaces. Since then many authors includingAndrijević have studied this class of sets by defining theirneighborhoods, separation axioms and functions. The purpose ofthis paper is to provide the new characterizations ofsemi-preopen and semi-preclosed sets by defining the concepts ofsemi-precontinuous mappings, semi-preopen mappings,semi-preclosed mappings, semi-preirresolute mappings,pre-semipreopen mappings, and pre-semi-preclosed mappings andstudy their characterizations in topological spaces. Recently,Dontchev (1995) has defined the concepts of generalizedsemi-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 usingsemi-generalized closed (sg-closed) sets and semi-generalized open(sg-open) sets due to Bhattacharyya and Lahiri (1987) intopology. In this paper for gsp-closed (resp., gsp-open)sets, we also introduce and study the concepts of approximatelysemi-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-preirresolutemappings to study the characterizations of semi-pre-T1/2 spaces defined by Dontchev (1995).