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Keywords: γ-continuity , weak-continuity , faint-continuity , u-weak-continuity , γ-open (γ-closed) , θ-open (θ-closed) , weakly-compact.
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In this paper, a new class of functions called “almost 3-continuous ” is introduced and their several properties are investigated. This new class is also utilized to improve some published results concerning weak continuity  and 3-continuity .