- #1

guhan

- 43

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How to say a given space is a manifold?

The only thing that props in my mind is to check if every open set has a euclidean coordinate chart on it. But, what if the space I am dealing with is not fully understood apriori?

As in, how were the spaces of thermodynamic equilibrium states, phase and configuration spaces in classical mechanics, space-time (of general relativity) etc given a manifold structure? How to justify that every open set of these spaces correspond to an euclidean space?

The only thing that props in my mind is to check if every open set has a euclidean coordinate chart on it. But, what if the space I am dealing with is not fully understood apriori?

As in, how were the spaces of thermodynamic equilibrium states, phase and configuration spaces in classical mechanics, space-time (of general relativity) etc given a manifold structure? How to justify that every open set of these spaces correspond to an euclidean space?

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