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Results tagged with continuum-theory
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user 25510
For questions from continuum theory. A continuum is a compact connected metric space (sometimes this term is used for a compact connected Hausdorff space).
2
votes
Planar compact connected set whose boundary has a finite length is arcwise connected
The answer is positive. First suppose that
$K=\partial K$. I will show that in this case
$K$ is the image of a curve.
By definition of Hausdorff measure, for every $\epsilon>0$ we can cover $K$ with o …
- 91.8k
3
votes
The number of components of the preimage of a continuum for a polynomial
Yes, you can. First construct a Jordan domain $D$ which contains
your continuum and does not contain any critical values. (To do this map the simply connected domain $\overline{\mathbf{C}}\setminus N$ …
- 91.8k