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In this paper induced U-equivalence spaces are introduced and discussed. Also the notion of U- equivalently open subsets of a U-equivalence space and U-equivalently open functions are studied. Finally, equivalently uniformisable topological spaces are considered.
In this paper we introduce two classes of functions called weakly preopen and weakly preclosed functions as generalization of weak openness and weak closedness due to [26] and [27] respectively. We obtain their characterizations, their basic properties and their relationshisps with other types of functions between topological spaces.
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