# Topological space proof

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

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#### 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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