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Recall the following definition: For X a topological space, and for A ? X, we define...

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Advance Math

Recall the following definition: For X a topological space, andfor A ? X, we define the closure of A as cl(A) = ?{B ? X : B isclosed in X and A ? B}. Let x ? X. Prove that x ? cl(A) if and onlyif every neighborhood of x contains a point from A. You may not useany definitions of cl(A) other than the one given.

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