The Kline sphere characterization, proven by Bing:
A compact connected (nonempty) metric space (with at least two points) is the 2-sphere if and only if every circle separates and no pair of points does.
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The Kline sphere characterization, proven by Bing: A compact connected (nonempty) metric space is the 2-sphere if and only if every circle separates and no pair of points does. |
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