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Feb
18
comment Cycling Digits puzzle
@DavidConrad Yes the number is assumed to be in base $10$.
Feb
18
comment A closed ideal in a commutative Banach algebra $C(X)$
@DanielFischer To me it looks as if for any $f$ not in $I(x)$ you can just find an epsilon ball in the $\sup$ norm to show the complement of $I(x)$ is open. But then all the additional assumptions are not needed (like "natural" and that $K$ is Hausdorff and the thing about the characters).
Feb
16
comment Why are isometries continuous?
Like this: $$ \|f(x) - f(y)\| = \|x - y\| < \delta = \varepsilon$$
Feb
16
comment Why are isometries continuous?
If $f$ is an isometry (=distance preserving) then you can use $\delta = \varepsilon$ to prove $f$ is continuous.
Jan
29
comment O'Neill Formula in terms of Exterior Derivative of Killing Form
I couldn't agree more with your profile: Hatcher is not a great book, even before cohomology. At least according to my taste. Enjoy Kreyszig, I have not finished it but I found the parts that I did read very enjoyable and enlightening.
Jan
28
comment Seifert matrices — Figure 8 knot
Thank you for your comment. I will have to look into it when I have more time.
Nov
19
comment Prove Continuous functions are borel functions
I don't know off the top of my head. You might want to post your comment as a question.
Nov
15
comment Roadway and book recommendations to math study.
@AlexanderGruber While the article in the paper is an interesting piece of research could you please elaborate on what it has to do with the question? The question seems to be of the sort "I would like to understand A, B and C. My background is X. Could you please give me help on how to understand A, B and C, given my background" and I can't work out how an article on self-definition pertains.
Sep
25
comment Relation between primary ideal and prime ideal
@leducquang Can you give me a list of all prime ideals containing $q$?
Sep
23
comment Relation between primary ideal and prime ideal
@leducquang If $p^2 \subsetneq q \subsetneq p$ then neither $q=p^2$ nor $q=p$ but there are no powers of $p$ between $p$ and $p^2$ so therefore $q$ is not equal to a power of $p$.
Aug
18
comment Norms Induced by Inner Products and the Parallelogram Law
@Kits89 It was a typo. I corrected it. Is it clear now?
Jul
10
comment Complete list of Sierpiński's publications
Do you think one could circumvent the "copyright infringement" problem by somehow making the content of the papers available? I mean something like texing a purchased scan and slightly changing the wording of the paper. A joint effort of mathematicians around the world doing this seems more likely to happen than the unicorn they are talking about in the article.
Jun
21
comment Connected sets.
@mathusiast In $[0,1]\cup[2,3]$ both $[0,1]$ and $[2,3]$ are open. To see this, try to apply the definition of open: pick a point $x$ in $[0,1]$ and try to find an open ball around it that is contained in $[0,1]$. Of course this is possible for all points in $(0,1)$...
Jun
16
comment Intersection of all neighborhoods of zero is a subgroup
@LJR I can't think of any reference. Perhaps I should have written $(0,0)$ where I wrote $0$ to be less confusing. The open sets of a product of two topological spaces $T \times T'$ are precisely the sets of the form $O \times O'$ where $O$ and $O'$ are open in $T$ and $T'$ respectively.
Jun
6
comment Follow up on “Proof of $X \times X \hookrightarrow X$ implies $[X]^2 \hookrightarrow X$”
Thanks for the upvote that reminded me of this question!
Jun
2
comment Complete list of Sierpiński's publications
I did miss it, thank you for the link. Sadly, it very much sounds like it's not going to happen within the next 5 years. But It's good to know that someone else is doing it.
Jun
2
comment Possible mistake in Specker's thesis
@BrianM.Scott $h$ is assumed to map $H$ to itself. But I don't see how it follows for all transpositions of $a^\ast$.
Jun
2
comment Possible mistake in Specker's thesis
@BrianM.Scott Done.
Jun
2
comment Possible mistake in Specker's thesis
@BrianM.Scott "...$e$ eine endliche Teilmenge von $a$...". Or would it be better if I also copy pasted that part?
Jun
1
comment Permutation models: when are they isomorphic?
Regarding the statement in your last sentence: is the proof of it something a first year grad student can figure out with a bit of thinking or would it be wise if I kindly requested you to point me to a book (or paper) where I can read a proof? Perhaps my problem is not the actual proof but making the connection between the topology and truth of statements in the model so perhaps I should ask for a reference to that?