Abstract:
Every topological space is a closure space, if we define the closure operator of the space as a function that takes any subset to its closure. This paper presents an introduction toCech closure space. The set of all Cech closure operators on a set is closed under the operations of union.Weinitiate Contra pgb - continuous maps, Contrapgb - irresolute maps.Furthermore we extend and study their characterizations.At every places the new notions have been substantiated with suitable examples.We also investigate the relationships among such functions.

Keywords: Contra pgb - continuous and Contra pgb - irresolute functions,totally continuous,pgb - open map.