We study the so-called Co-F-Closed and Almost Co-F-Closed Topologies of a given topological space. Several results which have appeared in [4] are expanded and improved. Also, we introduce and study a new class of functions y, almost F-continuous topological spaces, namely almost F-continuous functions which property contains the class of F-continuous functions (Chae et al., [4]). We also show that the concept of almost F-continuity can be considered naturally from the point of view of change of topology.
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