All Questions
Tagged with mg.metric-geometry metric-spaces
159 questions
18
votes
1
answer
4k
views
reference for "X compact <=> C_b(X) separable" (X metric space)
I know (and am able to prove via Stone-Čech compactification) that the following is correct:
Theorem: A metric space is compact if and only if its space of bounded, continuous, real-valued ...
- 888
16
votes
5
answers
903
views
Which metric spaces have this superposition property?
Let $A \subset X$ and $B \subset X$ be two isometric subsets of a metric space $X$. So there is an isometry $f: A \to B$.
Say that a metric space $X$ has the superposition property (my terminology) ...
- 151k
6
votes
1
answer
333
views
Trasportation metric (AKA Earth-Mover's, Wasserstein, etc.) as "natural" / "induced"?
Context: Given a discrete finite metric space $X$ (in my case X={0,1}$^n$ with the Hamming/L$_1$ distance), I need to define the natural or canonical metric on the set of all probability distributions ...
- 111
9
votes
3
answers
836
views
What makes a distance?
In the answers to my previous question, I learned that there are different concepts of distance, that is of distance-like functions with the usual metric being only the most popular and important one.
...
- 9,720
4
votes
1
answer
1k
views
Length spaces with continuous length functional: is this set Gromov-Hausdorff closed?
As far as I can tell, a major motivation for the study of length spaces is that they arise as Gromov-Hausdorff limits of Riemannian manifolds. Specifically,
A complete connected Riemannian manifold ...
- 3,212
0
votes
1
answer
526
views
How the distance between sets is called?
Hello,
I've recently write down some measure for sets and now I wonder how it is called or where it is described?
The measure itself is the following:
Let $A$ & $B$ -- two sets of values from a ...
- 103
1
vote
3
answers
688
views
How to show the cardinality of nonisometric compact metric spaces is the continuum
It is asserted in A Course in Metric Geometry by Burago, Burago, Ivanov that
there can be no more than continuum of mutually nonisometric compact spaces
How is this proven?
Its clear that there ...
- 7,197
15
votes
3
answers
7k
views
A metric for Grassmannians
I'm reading an article by Ricardo Mañé, "The Hausdorff dimension of horseshoes of diffeomorphisms of surfaces" (https://doi.org/10.1007/BF02585431). I'm having a technical problem. Sorry for ...
user11178
10
votes
1
answer
560
views
Are packing-homogeneous spaces homogeneous?
Given a metric space (M,d) define the packing function P(x,R,r) to be the maximum number of non-intersecting balls of radius r with centers in the ball B(x,R). Let’s call M packing-homogeneous if the ...
