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    Topological space proof

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    Let (Y,T) be a top. space where A is a subset of Y. Show that int(Y-A) = Y - A'

    © BrainMass Inc. brainmass.com October 10, 2019, 2:25 am ad1c9bdddf
    https://brainmass.com/math/discrete-math/topological-space-proof-376722

    Solution Preview

    First, let's give the relevant definitions:
    x is in the interior int(X) of X if there's an open set U such that x is in U and U is contained in X.
    x is in the closure X' of X if for any neighborhood V of x, the intersection of V and X is not empty.

    Negate the statements above to get:
    x is in the _complement_ Y(int(X)) of int(X) if every open set ...

    Solution Summary

    This posting shows that the interior of the complement to a set is the complement to the closure of the set.

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