By the connectedness, there is a continuous path between two points x and y, and by compactness I can find a finite open covering discs of this path, then I can easily construct a smooth function in the union of these discs. But how to deal with the injectivity ?Construct a smooth injective ( the path do not cross itself)path?
2026-04-08 22:20:07.1775686807
Constructing a smooth injective path between two points in a connected open subset of $\mathbb{R}^2$
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