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 Yearling
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Jan
21
comment Is Fredholm operator always a closed map?
I think you are right and my memory is wrong, thanks!
Jan
20
comment Is Fredholm operator always a closed map?
@Alessio Pellegrini No, your statement is true only in the Hilbert space case, and there are counterexamples for general case, first given by Rudin if I remember right. (I know this later after I asked this question on stackexchange.)
Dec
3
comment Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
@Myself Thank you very much for the idea of DCC.
Dec
3
comment Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
@Myself Could you say some more details?
Dec
3
revised Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
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Dec
3
revised Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
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Dec
3
comment Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
@Marc van Leeuwen In fact the link I gave is countable group. But if you regard any group as a Lie group with the discrete topology, a genuine Lie group have positive dimension would seems weird.
Dec
3
comment Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
@Marc van Leeuwen Sorry for the typo, fixed now.
Dec
3
comment Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
@Marc van Leeuwen But this is not interesting, a Lie group is a manifold, so we usually require it to have a countable basis for its topology.
Dec
3
revised Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
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Dec
3
revised Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
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Dec
3
suggested rejected edit on Conjugate subgroup strictly contained in the initial subgroup?
Dec
3
asked Under what mild condition, inclusion of a conjugate subgroup in the initial subgroup gives equality?
Dec
3
comment A subgroup such that every left coset is contained in a right coset.
If $xH \subseteq Hy$ for some $x, y \in G$ (not all), then can we still have $xH = Hy = Hx$?
Sep
19
awarded  Yearling
May
14
comment Dirichlet problem in the disk: behavior of conjugate function, and the effect of discontinuities
@Yes You exhibit nice answer. I can understand your (counter)example intuitively but cannot write mathematically rigid for example with your 1st example for $F$, such as how the boundary arcs are maped by your conformal map $F$, where the imaginary part of $F$ goeswhen $z$ tends to other point except the two points on the boundary of the unit disk which are sent into infinity by $F$? Can you explain a little?
May
13
revised Should a certain entire function be a polynomial?
edited tags
May
13
answered Is the set of $f\colon U \to \mathbb C$ with $f(z_0) = -1$ and $f(U) \cap \mathbb Q_{\geq 0} = \emptyset$ a normal family?
May
13
revised Should a certain entire function be a polynomial?
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May
13
revised Should a certain entire function be a polynomial?
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