In this paper, we introduce a new function called tri-ĝ continuous in tri-topological spaces. A map f : X → Y is called tri-ĝ continuous if f-1(V) is tri-ĝ closed in X for each tri-closed set V in Y. Also we define, quasi tri-ĝ. perfectly tri-ĝ, contra tri-ĝ, totally tri-ĝ and strongly tri-ĝ continuous maps are introduced and some of their properties are studied.
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