Mathematics, 26.01.2021 23:50 375025

Let X be a topological space and let C and U be subsets of X. Define C to be closed if C contains all its limit points and define U to be open if every point p ∈ U has a neighborhood which is contained in U. Assuming these definitions show that the following statements are equivalent for a subset S of X. i) S is closed in X; ii) X – S is open in X; iii) S = [S].

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Let X be a topological space and let C and U be subsets of X. Define C to be closed if C contains al...