bio | website | |
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location | Nicosia, Cyprus | |
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visits | member for | 1 year, 9 months |
seen | Jun 13 at 9:15 | |
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Department of Mathematics & Statistics of the University of Cyprus
Apr
29 |
awarded | Necromancer |
Feb
16 |
awarded | Custodian |
Feb
14 |
revised |
Inserting an open and simply-connected set between a compact set and an open set
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Feb
11 |
revised |
Inserting an open and simply-connected set between a compact set and an open set
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Feb
11 |
revised |
Inserting an open and simply-connected set between a compact set and an open set
added 84 characters in body |
Feb
11 |
comment |
Inserting an open and simply-connected set between a compact set and an open set
$K$ is compact with connected complement in $\mathbb C$. |
Feb
11 |
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Inserting an open and simply-connected set between a compact set and an open set
This example fails to have connected complement. |
Feb
11 |
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Inserting an open and simply-connected set between a compact set and an open set
In the paper, $K$ is required to be a compact subset of $\mathbb C$ with a connected complement, i.e., not even connected. But if we further assume that $K$ is connected, then $K$ becomes simply connected (in the standard algebro-topological sense). |
Feb
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Inserting an open and simply-connected set between a compact set and an open set
But this $K$ is not simply connected! Neither its complement is connected. |
Feb
11 |
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Inserting an open and simply-connected set between a compact set and an open set
If the boundary of $K$ is sufficiently smooth, then the tubular neighbourhood works. But when $K$ has a non-smooth boundary, one can construct a counterexample, where for every $\varepsilon>0$, the corresponding tubular neighbourhood is not simply connected. |
Feb
11 |
asked | Inserting an open and simply-connected set between a compact set and an open set |
Dec
29 |
awarded | Popular Question |
Dec
4 |
awarded | Yearling |
Nov
13 |
revised |
Applications of the Small and Great Theorems of Picard
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Nov
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Applications of the Small and Great Theorems of Picard
Yes, I know this since I asked this question as well, and I have mentioned it in the OP. |
Nov
13 |
asked | Applications of the Small and Great Theorems of Picard |
Sep
24 |
awarded | Autobiographer |
Aug
29 |
awarded | Famous Question |
Aug
1 |
revised |
Diagonalization via the Toda flow
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Aug
1 |
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Diagonalization via the Toda flow
No, the are not available. I am trying to LaTeXify them. It was from a course taught at Courant by Percy Deift. |