Atik ([9]) under the name of ${\gamma}-open $ sets. This class is closed under arbitrary
union. The aim of this paper is to use ${\Lambda}-sets $ and ${\vee}-sets $ due to Maki ([15])
some topologies are constructed with the concept of b-open sets. $ b-{\Lambda}-sets,\; b-
{\vee}-sets $ are the basic concepts introduced and investigated. Moreover, several types of
near continuous function based on $ b-{\Lambda}-sets,\; b-{\vee}-sets $ are constructed and …