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Results tagged with gn.general-topology
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user 1162
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
5
votes
2
answers
385
views
Dimension of fibers under continuous maps
Is the following true? If yes, is there a simple way to show it?
Let $F:U \to \mathbb{R}^m$ be continuous, where $U$ is an open subset of $\mathbb{R}^n$. If $2 \leq m<n$, then there exists a fiber con …
- 2,154
13
votes
3
answers
713
views
How bad can a circle domain get?
Let $X$ be a domain in the Riemann sphere $\widehat{\mathbb{C}}$. We say that $X$ is a circle domain if every connected component of its boundary is either a circle or a point.
It was conjectured by …
- 2,154
2
votes
0
answers
126
views
Homeomorphic extension to totally disconnected sets
Dear Mathoverflow Community,
I am looking for a reference for the following topological fact:
Fact
Let $E$ and $F$ be two totally disconnected compact subsets of the plane (can assume perfect if yo …
- 2,154
2
votes
0
answers
79
views
On the (Brouwer-Koebe) Continuity Method
The so-called Continuity Method is a simple yet powerful method to show that a given continuous injective map is surjective. Namely, suppose that $f:X \to Y$ is a map between two connected manifolds $ …
- 2,154