What is a Jordan Region? I can't find the definition anywhere. The question asked, if $E\subset \mathbb{R}^n$, bounded and with finitely many accumulation points, then $E$ is Jordan region.
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$\begingroup$From pg. 384 of An Introduction to Analysis (3rd Edition) by William R. Wade:
12.3 Definition. Let $E$ be a subset of $\mathbb{R}^n$. Then $E$ is said to be a Jordan region if and only if given $\epsilon > 0$ there is rectangle $R \supseteqq E$, and a grid $\mathcal{G} = \lbrace R_{1}, \ldots, R_{p} \rbrace$ on $R$, such that
$$ V(\partial E; \mathcal{G}) := \sum_{R_{j} \bigcap \partial E \neq \emptyset} |R_{j}| < \epsilon. $$
... Thus a set is a Jordan region if and only if its boundary is so thin that it can be covered by rectangles whose total volume is as small as one wishes.
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