In this paper we consider new weak and strong forms of γ-irresoluteness and γ-closure via the concept of gγ-closed sets which we call ap-γ-irresolute, ap-γ-closed and contra-γ-irresolute maps. Moreover, we use ap-γ-irresolute and ap-γ-closed maps to obtain a characterization of γ − T 1 2 -spaces.

The concept of pairwise S-closedness in bitopological spaces has been introduced and some properties of such spaces have been studied in this paper. EY WORDS AND PHRASES. Pairwise semi-open, Pairwise almost compact, Pairwise S-closed, Pairwise regularly open and regularly closed, Pairwise extremal disconnectedness, Pairwise semi-continuous and irresolute functions. 1980 AMS MATHEMATICS SUBJECT ...

In this study, we investigate the further properties of quasi irresolute topological groups defined in [20]. We show that if a group homomorphism f between quasi irresolute topological groups is irresolute at $e_G$, then $f$ is irresolute on $G$. Later we prove that in a semi-connected quasi irresolute topological group $(G,*,tau )$, if $V$ is any symmetric semi-open neighborhood of $e_G$, then...

A.Pushpalatha et al [11] introduced the concept of τ-g-closed set in topological spaces. S.Eswaran and A.Pushpalatha [6] introduced and studied the properties of τ-generalized continuous maps and τ-gc-irresolute maps in topological spaces. In this paper, we introduce and study a new class of maps called τ-generalized open maps and the notion of τ-generalized homeomorphism and τ-gchomeomorphism ...

The aim of this paper is to introduce a new class of sets called (i,j) r^g closed sets and a new class of maps called D^(i,j) continuous maps and D^(i,j)irresolute maps in bitopological spaces. Also we introduce some new spaces called (i,j) – T^1/2 , (i,j) ^T 1/2 ,*T^1/2, ^T*1/2 and ^Trg and obtain their basic properties. Mathematics Subject Classification: 54A10

in this study, we investigate the further properties of quasi irresolute topological groupsdened in [20]. we show that if a group homomorphism f between quasi irresolute topologicalgroups is irresolute at eg, then f is irresolute on g. later we prove that in a semi-connectedquasi irresolute topological group (g; ; ), if v is any symmetric semi-open neighborhood ofeg, then g is generated by v...

In this present paper, by utilizing ij−δ semi open sets, we introduce ij−∧δ, ij−∨δ, g− ij−∧δ, g− ij−∨δ sets and investigate some of their properties in bitopological spaces. Also, we present and study the notions of ij − T∨sδ space, ij−∧δ continuous, ij−∧δ irresolute, ij−∧δ open and ij−∧δ homeomorphism functions.