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Dhanya. R^{1} and A. Parvathi^{2}

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In this paper using Ã¯ÂÂ°gb*closed set in topological spaces due to Dhanya R and A Parvathi [22] we introduced a new class of functions in a topological spaces called Ã¯ÂÂ° generalized b*continuous functions (briefly Ã¯ÂÂ°gb* continuous functions). Further the concept of almost Ã¯ÂÂ°gb*continuous function and Ã¯ÂÂ°gb*irresolute function are discussed
Keywords 
πgb*continuous function, πgb* irresolute function, almost πgb*continuous function. 
INTRODUCTION 
Generalized open sets play a very important role in general topology and they are now the research topics of many researchers worldwide. Indeed a significant topic in general topology and real analysis concerns the variously modified forms of continuity, separation axioms etc., by utilizing generalized open sets. Levine [4] introduced the concept of generalized closed sets in topological spaces. Since then many authors have contributed to the study of the various concepts using the notion of generalized bclosed sets. New and interesting applications have been found in the field of Economics, Biology and Robotics etc. Generalized closed sets remains as an active and fascinating field within mathematicians. 
RELATED WORK 
Levine [4] and Andrijevic [1] introduced the concept of generalized open sets and bopen sets respectively in topological spaces. The class of bopen sets is contained in the class of semipreopen sets and contains the class of semiopen and the class of preopen sets. Since then several researches were done and the notion of generalized semiclosed, generalized preclosed and generalized semipreopen sets were investigated in [2, 5, 10]. The notion of πclosed sets was introduced by Zaitsev [12]. Later Dontchev and Noiri [9] introduced the notion of πgclosed sets. Park [11] defined πgpclosed sets. Then Aslim, Caksu and Noiri [3] introduced the notion of πgsclosed sets. D. Sreeja and S. Janaki [7] studied the idea of πgbclosed sets and introduced the concept of πgbcontinuity. Later the properties and characteristics of πgbclosed sets and πgbcontinuity were introduced by Sinem Caglar and Gulhan Ashim [6]. Dhanya. R and A. Parvathi[22] introduced the concept of πgb*closed sets in topological spaces. 
PRELIMINARIES 
Throughout this paper (X, τ) represent nonempty topological spaces on which no separation axioms are assumed unless otherwise mentioned. For a subset A of a space (X, τ), cl(A) and int(A) denote the closure of A and the interior of A respectively. (X, τ) will be replaced by X if there is no chance of confusion. 
Definition 2.1 Let (X, τ) be a topological space. A subset A of (X, τ) is called 
The complements of the above mentioned sets are called semi open, αopen, preopen, semipreopen, regular open, bopen and b*open sets respectively. The intersection of all semi closed (resp. αclosed, preclosed, semipreclosed, regular closed and b closed) subsets of (X, τ) containing A is called the semi closure (resp. αclosure, preclosure, semipreclosure, regular closure and bclosure) of A and is denoted by scl(A) (resp. αcl(A), pcl(A), spcl(A), rcl(A) and bcl(A)). A subset A of (X,τ) is called clopen if it is both open and closed in (X, τ). 
CONCLUSION 
The study of πgb*continuous function is derived from the definition of πgb*closed set. This study can be extended to fuzzy topological spaces and bitopological spaces. 
References 
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