A New Approach of gamma-Open Sets in Bitopological Spaces

The main aim of this research paper is to introduce two weaker forms of (1, 2)-gamma-open set namely (1, 2)- gamma -semi-open set and (1, 2)-semi- gamma open set in bitopological space along with their several properties, characterizations and mutual interrelationships. As applications to (1, 2)- gamma -semi-open set and (1, 2)-semi- gamma open set we introduce (1, 2)- gamma -semi-continuous and (1, 2)-semi- gamma - continuous functions and obtain some of their basic properties. In this present work it is proved that among the two topologies if one of the topology is weaker than other then every (1, 2)- gamma -semi-open set is τ1-semi-gamma -open set. Lastly we show the interrelationships with (1, 2)*- gamma -semi-continuous and (1, 2)*-semi-gamma - continuous functions and the newly defined functions.