Let E be a subset of(adsbygoogle = window.adsbygoogle || []).push({}); R^{2}that is non-empty, compact, and connected. Suppose furthermore that E is the union of a countably infinite number of almost disjoint closed cubes {R_{i}} with non-zero volume.

Is there anything interesting about this set, particularly its boundary? Can it have infinite length, for example? I can't think of very much to say about it, at all.

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# The Boundary of a Countable Union of Almost Disjoint Cubes

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