Tagged Questions
3
votes
0answers
74 views
Lipschitz continuity for an iterated function system
Let $(M,d_M)$ and $(N,d_N)$ be metric and
$$
CB(M)=\{\mbox{all closed bounded subsets of }M\}.
$$
Let $f: M\to N$ be a Lipschitz map with Lipschitz constant $L$. Define a map
$$
F:(CB(M),\rho)\to ...
0
votes
1answer
141 views
Finite sets are dense with respect to Hausdorff distance
Let $(X,d)$ be a complete metric space and consider
\begin{align*}
BC(X)&=
\lbrace C\subset X\;|\;C\neq\emptyset\text {, closed and bounded} \rbrace\cr
\mathrm{Fin}(X)&=
\lbrace ...
3
votes
0answers
106 views
Is the Hausdorff semi-distance Lipschitz?
Let $X$ be Banach (with metric $d$) and let $H(X)$ be the set of closed bounded subsets of $X$. Define for $A,B\in H(X)$ $$\delta(A,B)=\sup_{a\in A}\inf_{b\in B}d(a,b)$$ be the Hausdorff semi-distance ...
