Let \(X\) be a topological space and \(A\subseteq X\). A point is in \(\Int A\) if and only if it has a neighbourhood contained in \(A\).
Proof
This is an immediate consequence of the definition of the interior
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Let \(X\) be a topological space and \(A\subseteq X\). A point is in \(\Int A\) if and only if it has a neighbourhood contained in \(A\).