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Mathematics, 28.12.2020 04:20 YEOng

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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