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## Homework Statement

If p has a neighborhood contained in A, then p is in the interior of A.

## Homework Equations

Int A = [itex]\bigcup[/itex]{C[itex]\subseteq[/itex]X:C[itex]\subseteq[/itex]A and C is open in X}

By the books definition, a neighborhood is open.

## The Attempt at a Solution

Let C'[itex]\subseteq[/itex]A be a neighborhood of p contained in A

Then p[itex]\in[/itex][itex]\bigcup[/itex]{C[itex]\subseteq[/itex]X:C[itex]\subseteq[/itex]A and C is open in X}

p[itex]\in[/itex]Int A

Seems too simple, but I'm going through the book's definition of "neighborhood of p"--and open subset of X.

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