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What are the Equivalent Topological Definitions?
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Let $A \subseteq \mathbb{R}^n$.
\begin{enumerate}
\item A is closed iff $A' \subseteq A$
\item $\bar{A} = A' \cup A$
\item $A^0$ is equal to the set of all interior points of A
\item $\partial A = \bar{A} \setminus A^0$
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