I was reading this question, and I idly wondered if there could be spaces that were globally Euclidean, but locally not, and couldn't think of any circumstances in which that might be the case.
Are there spaces that are globally Euclidean, but locally not?
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4What does it mean to be globally Euclidean? – 2010-12-09
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0Please define globally Euclidean. – 2010-12-09
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0Qiaochu beat me to it :-) Anyway, once you have (somehow) defined globally Euclidean, define locally Euclidean. Chances are that that will settle your question. – 2010-12-09