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 Curious
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Jul
2
awarded  Curious
Nov
30
comment Is there a conformal self-map on the upper half-plane that swaps two points?
Oh, right, it may be better to think about this on the unit disk since it and the upper half-plane are isomorphic. I'll see what I can cook up, thanks.
Nov
30
asked Is there a conformal self-map on the upper half-plane that swaps two points?
Nov
18
awarded  Commentator
Nov
16
comment Möbius map from circles to lines
I tried the second question using the cross ratio, but it doesn't tell me much, just that the ratio is real (which we already knew). I'm thinking now that I want to prove there is a line that that the four points are symmetric in pairs with respect to. Then if I map that line to the imaginary axis, I'll get symmetric points $\pm a, \pm b$ which I can scale down as appropriate.
Nov
16
accepted Möbius map from circles to lines
Nov
16
comment Möbius map from circles to lines
That's what I did. Before, I tried mapping the imaginary axis to the real axis and $-2 \mapsto \infty$, since this would be the desired configuration, by $4i \mapsto 1, 0 \mapsto 0$. This didn't work, though. Turns out I had to do $4i \mapsto 0, 0 \mapsto 1$, which, I guess, had the same orientation as the original circles.
Nov
16
revised Möbius map from circles to lines
added 158 characters in body
Nov
16
asked Möbius map from circles to lines
Nov
11
revised Alternate form of the Residue theorem?
added 20 characters in body
Nov
10
asked Alternate form of the Residue theorem?
Nov
9
accepted Rewrite a series as a power series?
Nov
9
asked Rewrite a series as a power series?
Oct
20
accepted Why is the intersection of a clopen set and another set clopen in this proof?
Oct
20
comment Why is the intersection of a clopen set and another set clopen in this proof?
Oooooh, sorry, I misread. Any subset is clopen in its subspace topology, but certainly not in the subspace topology of $W_{\alpha_0}$. I managed to confuse myself with subsets and subspaces.
Oct
20
comment Why is the intersection of a clopen set and another set clopen in this proof?
I thought that might be the case, but isn't any subset of $W_{\alpha_0}$ clopen in the subspace topology?
Oct
20
asked Why is the intersection of a clopen set and another set clopen in this proof?
Oct
1
awarded  Scholar
Oct
1
accepted Find entire functions that satisfy certain conditions
Oct
1
comment Find entire functions that satisfy certain conditions
In the first that inequality holds for any $z$ by uniform continuity. But since the LHS holds for any smaller choice of delta, it holds in the limit as $\delta \to 0$. So I concluded that the derivative was bounded, though now I see that your comment above concerned this very conclusion and I haven't used LVK's fact about that difference being entire. With the integral, by induction and the Gauss MVT I conclude that $f^{(n-1)}(0) = 0$ for all n. So by uniqueness, it must be identically zero on the unit disk, and therefore zero on the entire plane.