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 Yearling
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1d
accepted Proving $\mathbb{R}^2$ is not homeomorphic to $\mathbb{R}^3$
Feb
2
asked Existence of a curve with index 1 around a compact set
Jan
11
awarded  Yearling
Dec
21
asked Examples of a Banach space with an algebra structure having only left continuity
Dec
18
accepted Possible analytic images of the unit disc?
Dec
15
comment Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space.
I am not looking for a proof of the first statement. I just made it to illustrate how I thought of this question.
Dec
15
revised Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space.
corrected a wrong assumption
Dec
15
revised Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space.
added 4 characters in body
Dec
15
awarded  Informed
Dec
15
asked Maximum number of 1-separated points in the unit ball of an $n$-dimensional Banach space.
Dec
15
comment Invertible elements in Banach algebra.
hint: try thinking about what $(xy)^{-1}$ should be if $x,y$ are invertible.
Dec
14
accepted Want to construct a polynomial with specific properties.
Dec
14
comment Want to construct a polynomial with specific properties.
Rouche's theorem says that if $|f(z)|<|g(z)|$ on the curve, then $f$ and $f+g$ have the same number of zeros inside the curve. I wanted to know if the theorem holds even if $|f(z)|=|g(z)|$ just for a single point. If I get such a polynomial, then the answer is no.
Dec
14
revised Want to construct a polynomial with specific properties.
added 1 character in body
Dec
14
asked Want to construct a polynomial with specific properties.
Dec
14
asked Possible analytic images of the unit disc?
Dec
9
accepted Isometric copy of $\ell_1$ in $C[0,1]$?
Dec
5
comment Isometric copy of $\ell_1$ in $C[0,1]$?
Also, doesn't this proof only work for real $\ell_1$? If I were to extend this map to complex sequences, I think this fails to be an isometry. Is there a way to fix this?
Dec
5
comment Isometric copy of $\ell_1$ in $C[0,1]$?
I think you meant just $(\alpha_n-1)$, not $(2\alpha_n-1)$.
Dec
4
comment Isometric copy of $\ell_1$ in $C[0,1]$?
Could you point me to a reference for for that?