Rudy the Reindeer
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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? 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 $\mathbb{Q}(\sqrt{3},\sqrt{7})=\mathbb{Q}(\sqrt{3},\sqrt{21})$? 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. ${}$