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- Locally euclidean request in manifold definition

Hi,

I'm a bit confused about the locally euclidean request involved in the definition of manifold (e.g. manifold ): every point in ##X## has an open neighbourhood homeomorphic to the Euclidean space ##E^n##.

As far as I know the definition of homeomorphism requires to specify a topology for both spaces (here the open neighbourhood as a space itself and the Euclidean space ##E^n##). Are the two spaces "silently" supposed to be endowed each with the subspace topology ?

I'm a bit confused about the locally euclidean request involved in the definition of manifold (e.g. manifold ): every point in ##X## has an open neighbourhood homeomorphic to the Euclidean space ##E^n##.

As far as I know the definition of homeomorphism requires to specify a topology for both spaces (here the open neighbourhood as a space itself and the Euclidean space ##E^n##). Are the two spaces "silently" supposed to be endowed each with the subspace topology ?

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