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Mathematics, 03.01.2021 04:00 ineedtopeebeforethec
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 a...
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