In this article we discuss the nature of contra-continuous functions in the generalized topological space via neutrosophic sets. Also we introduced a new type of set named as $\mu_N$ nowhere dense set and by making use of $\mu_N$ nowhere dense set we derive $\mu_N$ Baire Space and their features are to be discussed. The characters of $\mu_N$ rare sets also discussed briefly.
Keywords and Phrases
$\mu_N$ contra-continuous, $\mu_N$ perfectly continuous, $\mu_N$ dense sets, $\mu_N$ Rare set, $\mu_N$ Baire Spaces.
A.M.S. subject classiﬁcation
54C99, 54A99, 54G05.