Aim of this paper is to introduce and study the new type of homeomorphism, namely (?1, ?2)* - Q* homeomorphism and ?1?2 - Q* homeomorphism in bitopological spaces. Also we define (?1, ?2)* -irreducible spaces and ?1?2 - irreducible spaces. Here researchers proved that the set of all (?1, ?2)* - Q* homeomorphism forms a group.
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