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Department of Mathematics & Statistics of the University of Cyprus


Feb
16
awarded  Custodian
Feb
14
revised Inserting an open and simply-connected set between a compact set and an open set
deleted 6 characters in body
Feb
11
revised Inserting an open and simply-connected set between a compact set and an open set
added 7 characters in body
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
comment Inserting an open and simply-connected set between a compact set and an open set
This example fails to have connected complement.
Feb
11
comment 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
11
comment 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
comment 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
deleted 1 character in body
Nov
13
comment 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
added 5 characters in body
Aug
1
comment 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.
Aug
1
accepted Diagonalization via the Toda flow