Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [homeomorphism]

The tag has no usage guidance.

0
votes
0answers
37 views

The case of a redundant disjoint sum

I'm trying to calculate $\Sigma (\Gamma_{\sigma})$ as discussed on p.230 of 'Structured meanings and reflexive domains' by Serge Lapierre. Use '$\Sigma(\Gamma)$' to indicate the disjoint sum of all $...
1
vote
2answers
99 views

Extending homeomorphisms between compact metric subsets

Let $X$ be a compact metric, second countable space with finite covering dimension. Let $A,B$ be two closed subsets of $X$. Assume that $h:A\to B$ is a homeomorphism. Is it possible to extend $h$ to a ...
10
votes
1answer
183 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 ...
8
votes
2answers
217 views

Are there invariants of cell complexes similar to the Euler characteristic?

The Euler characteristic is an invariant (under homeomorphism) of manifolds that can be computed from a cellulation by (weighted) counting of different kinds of objects, namely \begin{equation} \chi=\...
4
votes
1answer
206 views

Automorphisms of Erdös spaces

It is well-known that there is an automorphism of the Cantor set $h:C\to C$ such that $\overline{\{h^n(c):n\in \mathbb Z\}}=C$ for every $c\in X$. In other words, there is a self-homeomorphism of $C$...
5
votes
2answers
235 views

generators for the handlebody group of genus two

Is the handlebody group of genus two surface generated by Dehn twists along properly embedded disks and annuli? Are there alternative ways to describe a set of generators that are conceptually simple ...
4
votes
0answers
126 views

Similarities between isomorphism classes of homeomorphic directed graphs

To clarify, I'm speaking of homeomorphisms in a graph theoretic context, defined by subdivisions of arcs in a directed graph. A subdivision of an arc $(x,z)$ in a directed graph is obtained by ...
1
vote
0answers
67 views

Homeomorphism type of pair of faces in a regular CW complex

Let $X$ be a regular CW complex, $\sigma$ an $n$-dimensional cell of $X$ and $\tau$ an $(n-1)$-dimensional face of $\sigma$. Is it true that the pair $(\bar\sigma, \bar\tau)$ is homeomorphic to the ...
10
votes
3answers
349 views

Is an open subset of a rigid space rigid?

Let $X$ be a locally compact Hausdorff space. Call $X$ rigid if its only autohomeomorphism is the identity, $\operatorname{Homeo}(X)=\{1\}$. Questions: Let $X$ be rigid. Is it true that every open ...
10
votes
1answer
329 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 $\mathrm{Borel}(M)$ ...
5
votes
1answer
362 views

Proof of the stable homeomorphism conjecture

I would like to get a demonstration of the stable homeomorphism conjecture (SHC$_n$), stating that any orientation-preserving homeomorphism $\mathbb{R}^n \rightarrow \mathbb{R}^n$ is stable in ...
9
votes
2answers
329 views

Extending homeomorphisms from closed countable sets to S^2

Let $A, B \subset S^2$ be closed, countable sets and $\phi \colon A \rightarrow B$ be a homeomorphism. Can we extend $\phi$ to a homeomorphism from $S^2$ to itself? It is well-known that the answer ...