The definition of a topological manifold from Wikipedia: tm defines it as a topological space which locally looks like Euclidean space. But what about a topological space that uses the Minkowski metric from special relativity? It doesn't appear to be Euclidean locally, so does that mean it's not a topological manifold?
Is a topological space with a Minkowsi metric a topological manifold?
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3Locally Euclidean means *locally homeomorphic* to $\mathbb{R}^n$. This has nothing to do with the *(pseudo-)metric* structure. Could you specify what you mean by a topological space with the Minkowski metric? This doesn't make sense to me. – 2011-07-21
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1@Theo: I assume the OP means a pseudo-Riemannian manifold, or perhaps more specifically a Lorentzian manifold. – 2011-07-21
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0@Qiaochu: a pseudo-Riemannian manifold is a manifold... – 2011-07-21
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1@Qiaochu: well, yes. What I meant was "I assume the OP is not familiar with the precise definitions but is interested in relativity and therefore _wants_ the notion of a pseudo-Riemannian manifold." – 2011-07-21
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0Thanks for the comments which are all very useful. Rather than wasting people's time further, I'll bone up on "pseudo-Riemannian manifolds" – 2011-07-22