577 reputation
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location China
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visits member for 10 months
seen Jun 25 at 0:46

I am a student studying mathematics.


Jul
2
awarded  Curious
Jun
20
revised Fundamental group of the special orthogonal group SO(n)
added 51 characters in body
Jun
20
answered Fundamental group of the special orthogonal group SO(n)
Jun
8
comment Is Fredholm operator always a closed map?
Oh, I mean one that maps closed set to a closed one.
Jun
8
comment Is Fredholm operator always a closed map?
I don't think your claim is true, since in the definition of Fredholm operator, we usually need to assume the image $f(A)$ is closed in $F$.
Jun
8
asked Is Fredholm operator always a closed map?
May
10
revised The limit of the derivative of an increasing and bounded function is always $0$?
edited title
May
10
accepted The limit of the derivative of an increasing and bounded function is always $0$?
May
10
asked The limit of the derivative of an increasing and bounded function is always $0$?
May
6
revised Positive function approximation
added 2 characters in body
May
6
asked Positive function approximation
Apr
15
accepted Is the dual of a complete topological vector space always complete?
Apr
15
comment Is the dual of a complete topological vector space always complete?
What is $\sigma (X,X^*)$? Also, just now I found an exercise in a functional analysis book says that if the topology of $X$ is induced by (countably many) seminorms, then $X′$ is complete (even true when $X$ is not complete). Anyway, thank you!
Apr
15
comment Is the dual of a complete topological vector space always complete?
Oh, you mean the product topology on the product space. But I don't agree with one of your claims, just think about the Schwartz class, the space of rapidly decreasing functions, its topology is induced by countably many norms, and its dual, the space of tempered distributions, is complete yet.
Apr
15
comment Is the dual of a complete topological vector space always complete?
So the topology you give $\mathbb{C}^X$ is pointwise convergence? If I assume the topology of $X$ is induced by (countably many) seminorms, then is $X'$ complete?
Apr
15
asked Is the dual of a complete topological vector space always complete?
Mar
27
accepted Is the function $\frac{1}{\sqrt{|x_1|}}$integrable on the unit sphere $S^{n-1}\subset\mathbb{R}^n$?
Mar
27
comment Is the function $\frac{1}{\sqrt{|x_1|}}$integrable on the unit sphere $S^{n-1}\subset\mathbb{R}^n$?
So you mean there is the relation of measures: $d\sigma (x_{1}, \bar{x})=dx_{1}d\sigma (\bar{x})$? How can I deduce this relation? Can you explain or give some reference?
Mar
26
revised Is the function $\frac{1}{\sqrt{|x_1|}}$integrable on the unit sphere $S^{n-1}\subset\mathbb{R}^n$?
added 145 characters in body
Mar
26
asked Is the function $\frac{1}{\sqrt{|x_1|}}$integrable on the unit sphere $S^{n-1}\subset\mathbb{R}^n$?