Abstract
In this paper a new class of functions, such that semi –continuous function is introduced for topological spaces, and the second type is semi –continuous function and three class is semi –continuous function. We have taken in our study this continuous homeomorphism function (bijective = injective + surjective). we introduce using practical examples of mathematical formulas and considering them as a direct application to the validity of the observations. We also, study the relationship between these concepts that we referred to at the beginning of the research.
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