Samuel Handwich
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 Mar20 awarded Great Question Jan22 awarded Famous Question Dec23 awarded Good Question Dec20 awarded Yearling Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ I see, that is still very cool. Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ Anyway, I do like this non-Archimedean, even though it is pretty pathologic. Does it come up in another place sometimes? Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ I just say discrete metric is stupid because it is the easy example when you are wrong, but mostly it says nothing. It is like the trivial group, if you say all groups have non-trivial normal subgroup, the trivial group tells you no, but if you ask for a group with no non-trivial normal subgroups, the trivial group has one, but it is the stupid example. Maybe I am just not appreciate until I am old enough in analysis. Dec12 awarded Nice Question Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ @RossPure Can you explain "the set itself dilating"? I see $\epsilon$ gets bigger we get the points around and the compact sets, but I am confuse on how to see the set is dilate, do you mean take the union is still compact? Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ What is the well-known manifold? I think its triangle is the same one as Ivo Terek example. Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ This is very good, I think it is qualitate from a lot of the other. What are the metric properties for this metric (like compact and open sets)? Is there a page with the list? Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ I do like this little example very much :) Dec12 revised Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ added 38 characters in body Dec12 revised Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ added 38 characters in body Dec12 comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ @Bungo Maybe you can write some about how to see these, I have heard about but do not know a lot how they work. (I think this question has a few answers, but I hesitate to make big-list so that it will not be an opinion.) Dec12 revised Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ added 5 characters in body Dec12 accepted Riemann mapping theorem and an inequality inducing conformality Dec12 accepted Can I use Schwartz's Lemma to prove that $f(0)=0$ and $\operatorname{Re}f(z)\rightarrow 0$ implies $f(z)=0$ for all $z\in\mathbb{C}$? Dec12 asked Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$ Nov22 accepted What is the expected value of the mean of the highest $m$ numbers in a population of $N$ normally distributed random variables?