ABSTRACT:The aim of this paper is to introduce various functions associated with semi*α-open sets. Here semi*α-continuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characterizations for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are introduced and their properties are studied. In addition strongly semi*α-irresolute functions, contra-strongly semi*α-irresolute functions, semi*α-totally continuous, totally semi*α-continuous functions and semi*α-homeomorphisms are introduced and their properties are investigated.
In this paper, we introduce new concepts, namely semi*α-connectedness and semi*αcompactness using semi*α-open sets. We investigate their basic properties. We also discuss their relationships with already existing concepts of connectedness and compactness.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.