pathwise connected

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Connected space — For other uses, see Connection (disambiguation). Connected and disconnected subspaces of R² The green space A at top is simply connected whereas the blue space B below is not connected … Wikipedia
Diffeomorphism — In mathematics, a diffeomorphism is an isomorphism in the category of smooth manifolds. It is an invertible function that maps one differentiable manifold to another, such that both the function and its inverse are smooth. The image of a… … Wikipedia

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