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Dec
20
comment Properties of dual spaces of sequence spaces
I will have to read the whole thread and this answer as it's not even clear to me what pairing here means exactly. Sounds like either $f$ or $g$ is fixed because we probably want to show that these angle brackets (in one argument) define an isomorphism. But I won't have time to do this before tomorrow night.
Dec
20
comment Properties of dual spaces of sequence spaces
@AnthonyPeter That's an excellent question. I will have to think about this as I do not know the answer off the top of my head.
Dec
16
comment Contractible vs. Deformation retract to a point.
This I explain in the first paragraph of my answer. Pick a point in $Y$ and an $\varepsilon$ ball around it. Can you find a neighbourhood inside the ball that is contractible? I don't think so -- it's not even connected!
Dec
8
comment Let $S$ be a non-empty set with an associative, cancellative operation and for each $a\in S$, $\{a^n\}$ is finite, must S be a group?
Possible duplicate of Confused about this exercise question: if a set with a certain binary operation is a group
Dec
3
comment Examples of absolutely continuous functions that are not Lipschitz.
@FardadPouran Yes, as I point out in my comment above.
Nov
28
comment If an abelian group has more than 3 elements of order 2 then it must have at least 7 elements with order 2.
Alan's answer has been undeleted.
Nov
23
comment Orders of the elements in $\mathbb{Z}/8\mathbb{Z}$
You're confusing additive and multiplicative notation I suspect. The neutral element here is $0$ not $1$.
Nov
23
comment Cauchy Residue Theorem Application
Craig, I left a comment in response to your comment to my answer in another thread. Since you probably won't be notified (as you seem to have deleted your comment) I am notifying you here.
Nov
23
comment Examples of absolutely continuous functions that are not Lipschitz.
@Craig You are right, it's not clear at all, I only hint at how to show uniform continuity. It would have been much better to use Lebesgue integrability of the square root function as in definition (2) here‌​. I will edit the answer when I have time. Thanks a lot for pointing out this shortcoming.
Nov
21
comment Continuous function on a compact metric space is uniformly continuous
@shilov You should look at the last line of the proof. The inequality should explain it.
Nov
3
comment Fourier transform of the characteristic function
@user929304 I see. I don't know if it makes sense, this is beyond my modest knowledge of Fourier transforms. It's not very useful but: Surely the decaying properties of $\mathcal F (\chi_{[c,d]}$ and $\mathcal F (\chi_{[0,1]}$ are almost identical?
Nov
3
comment Fourier transform of the characteristic function
@user929304 It's not clear to me what you mean. For example, "not differentiable in the usual sense" -- well apart from the points $c,d$ its derivative is 0, or am I missing something? And as for the FT of $\chi_{[c,d]}$: It looks to me like it's decaying. The expression is term one minus term two where each term is of the form one over something exponential times linear. But I might be missing something, it's been a while.
Nov
3
comment invertibility in C*-algebra
I don't understand why you would try to prove that $a-\lambda$ is invertible if by assumption ($\lambda \in \sigma (a)$) it isn't. What is your question?
Nov
3
comment Is it true that $\mathbb{Q}(\sqrt{3},\sqrt{7})=\mathbb{Q}(\sqrt{3},\sqrt{21})$?
Related: math.stackexchange.com/q/93463/5798
Nov
2
comment Proving $2\mathbb Z$ is maximal ideal of $\mathbb Z$
@RobertoMilandro Yes, exactly.
Nov
2
comment Proving $2\mathbb Z$ is maximal ideal of $\mathbb Z$
Regarding your second sentence: It's not possible for any ideal in $\mathbb Z$ to have more elements than $\mathbb Z$.
Oct
29
comment Let $F\subseteq K $ and $V$ is a vector space over $K$ with a basis. What is the basis of $V$ over $F$?
So... $K$ is a field with a basis $e_i$? Does that mean $K$ is also a vector space?
Oct
3
comment Calculating $\int_\gamma \frac{1}{1+z^2}\,dz$
@Tom-Tom Great, thank you.
Oct
2
comment Calculating $\int_\gamma \frac{1}{1+z^2}\,dz$
What's a primitive function?
Oct
2
comment How to prove function $f(x,y)=\frac{1}{xy}$ is not uniformly continuous?
Nicely done. ${}$