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