Reputation
821
Next privilege 1,000 Rep.
Create new tags
Badges
5 12 26
Impact
~44k people reached

Mar
20
awarded  Great Question
Jan
22
awarded  Famous Question
Dec
23
awarded  Good Question
Dec
20
awarded  Yearling
Dec
12
comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
I see, that is still very cool.
Dec
12
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?
Dec
12
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.
Dec
12
awarded  Nice Question
Dec
12
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?
Dec
12
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.
Dec
12
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?
Dec
12
comment Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
I do like this little example very much :)
Dec
12
revised Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
added 38 characters in body
Dec
12
revised Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
added 38 characters in body
Dec
12
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.)
Dec
12
revised Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
added 5 characters in body
Dec
12
accepted Riemann mapping theorem and an inequality inducing conformality
Dec
12
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 $z\in\mathbb{C}$?
Dec
12
asked Nonobvious examples of metric spaces that do not work like $\mathbb{R}^n$
Nov
22
accepted What is the expected value of the mean of the highest $m$ numbers in a population of $N$ normally distributed random variables?