Characterization of covering maps via path-lifting property
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چکیده
A continuous map between topological f : X → Y is said to satisfy the path-lifting property if for any path p : [0, 1] → Y and any x ∈ f(p(0)) there exists a lifting p̃ of the path p with the intitial value x, i.e. there exists a path p̃ such that f ◦ p̃ = p and p̃(0) = x. Similarly, a smooth map between Riemannian manifolds f : X → Y is said to satisfy the rectifiable path-lifting property if the above definition holds for the rectifiable paths p(t). Suppose that f : X → Y is a local homeomorphism (resp. diffeomorphism) between topological spaces X and Y (resp. Riemannian manifolds X and Y ).
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