All Questions
4
questions
1
vote
0
answers
42
views
Continuous surjection from $X(D_n)$ onto $\operatorname{Homeo}_0(D_n)$
Let $n>1$ and let $\mathfrak{X}(D_n)$ denote the set of continuous vector fields on the closed disc $D_n\subseteq \mathbb{R}^n$. Let $\operatorname{Homeo}_0(D_n)$ be the set of homeomorphism of ...
- 5,001
11
votes
1
answer
911
views
Why are homeomorphism groups important?
For a compact metric space $X$ let $\mathcal H(X)$ denote the set of homeomorphisms in the compact-open topology (also generated by sup metric). It is known that $\mathcal H(X)$ is a Polish ...
- 2,993
10
votes
1
answer
202
views
homeomorphisms induced by composant rotations in the solenoid
Let $S$ be the dyadic solenoid.
Let $x\in S$, and let $X$ be the union of all arcs (homeomorphic copies of $[0,1]$) in $S$ containing $x$.
$X$ is called a composant of $S$.
It is well-known ...
- 945
11
votes
2
answers
536
views
Homeomorphisms vs Borel automorphisms
Let $\mathrm{Homeo}(M)$ and $\mathrm{Borel}(M)$ be the groups of homeomorphic and Borel automorphisms of a space $M$, respectively.
Question: Are $\mathrm{Homeo}(M)$ and $\mathrm{Borel}(M)$ ...
- 1,807