Tagged Questions
1
vote
1answer
65 views
Function extending a Lipschitz function
Let $X$ be a metric space with a metric $d$, let $E\subset X$.
We have a function $f:E \rightarrow \mathbb R$ satisfying for some $M>0$:
$$
|f(x)-f(y)|\leq M d(x,y) \quad \text{for } x,y \in E.
$$
...
2
votes
1answer
57 views
Hölderian path connectedness
Let $X$ be a complete metric space and $\alpha \in (0,1)$. Suppose that for every $x,y \in X$ there exists $z \in X$ s.t.
$$
d(x,z) \le \frac{1}{2^\alpha}d(x,y), \qquad d(y,z) \le ...
