- #1

Hodgey8806

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## Homework Statement

Let A be a topological space and let A[itex]\subseteq[/itex]X be any subset.

Show: If a point A is in the interior, then it has a neighborhood contained in A.

## Homework Equations

Neighborhoods are defined to be open in my book.

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

## The Attempt at a Solution

Let p[itex]\in[/itex]Int(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}

So, [itex]\exists[/itex] an open set C' s.t. p[itex]\in[/itex]C' and C[itex]\subseteq[/itex]A

Q.E.D.