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Existence of $M>0$ s.t. every $x,y\in K\subset U$ can be connected by a path $l$ s.t. $|l|<M|x-y|$ for compact & connect $K$ and bounded open $U$?
Inspired by the brilliant answer by Martin R: https://math.stackexchange.com/a/4679552/820472 to the question Does there exist $M>0$ such that every $x,y\in U$ can be connected by a path $l$ with $|...
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Does there exist $M>0$ such that every $x,y\in U$ can be connected by a path $l$ with $|l|< M|x-y|$ in an open, bounded and path-connect set $U$?
Let $U\subset\mathbb{R}^n$ be a bounded, open and path-connected set. Then every two $x,y\in U$ can be connected to each other by a polygonal chain $l$. I am wondering whether you could find an $M>...
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Given this definition of geodesic, does it have constant speed ? $f(r,t)=f(r,s)+f(s,t)$
Let $(X,d)$ be a metric space, and $x,y\in X$. In Probability Measures on Metric Spaces of Nonpositive Curvature, Sturm defines a geodesic joining $x$ and $y$ as some continuous path $\gamma :[a,b]\to ...
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