New Forms of Contra-Continuity in Ideal Topology Spaces

Abstract

In this paper, we apply the notion of $e$-$\I$-open sets \cite{Wadei6} in ideal topological spaces to present and study new classes of functions called contra $e$-$\I$-continuous functions, almost-$e$-$\I$-continuous, almost contra-$e$-$\I$-continuous, and almost weakly-$e$-$\I$-continuous along with their several properties, characterizations and mutual relationships. Relationships between their new classes and other classes of functions are established and some characterizations of their new classes of functions are studied. Further, we introduce new types of graphs, called $e$-$\I$-closed, contra-$e$-$\I$-closed, and strongly contra-$e$-$\I$-closed graphs via $e$-$\I$-open sets. Several characterizations and properties of such notions are investigated.