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## Homework Statement

I have been asked to prove the following statement:

An accumulation point of a set S is either an interior point or a boundary point of S.

Here is my attempt at a solution:

I started from the definition of accumulation points:

A point is an accumulation point ([tex]x_0[/tex]) when [tex] \forall\epsilon > 0, N_{\epsilon}'(x_0)\capA\neq[/tex]empty set

By using the definition of a deleted neighborhood:

[tex](N_\epsilon(x_0)-\{x_0\})\capA\neq[/tex]empty set

so [tex]\forall a \in S' a\inN_\epsilon(x_0), a \notin\{x_0\}, a \inA[/tex]

and that's as far as I got. I'm not sure where to go from here.