All Questions
Tagged with isometries metric-spaces
7 questions
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If all balls at $x$ and $y$ are isometric is there an isometry sending $x$ to $y$?
Let $(X,d)$ be a metric space and $x,y \in X$. Assume that for all $r > 0$ the balls $B_r(x)$ and $B_r(y)$ are isometric.
Is it true that there exists an isometry of $X$ sending $x$ to $y$?
16
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If all balls around two points are isometric... -- manifold version
This question is a natural follow-up of this other question, asked earlier today by wspin.
Let's say that a metric space $(X,d)$ has two poles if:
there are two distinct points $x$, $y$ such that ...
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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
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Isometric embeddings of metric spaces in Hilbert spaces
There are plenty of isometric embeddings of metric spaces in Banach spaces. Nevertheless, I have been unable to find any significant result on isometric embeddings into Hilbert spaces. My question is: ...
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Isometric embeddings of $c_0$ into metric spaces
Are there any nice and useful criteria or theorems which assert when a given metric space $M$ contains an isometric (not necessarily linear) copy of the Banach space $c_0$ or its unit ball $B_{c_0}$? (...
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If $X,X'$ have the same $\varepsilon$-packing numbers and $f:X \to X'$ surjective $1$-Lipschitz, then $f$ is an isometry
Let $(X, d)$ be a compact metric space.
We say that $\{x_1, \cdots, x_n\} \subseteq X$ is an $\varepsilon$-covering of $X$ if for any $x \in X$, there exists $i \in \{1, \ldots, n\}$ such that $d(x, ...
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Are two metric spaces isometric if they have the same $\varepsilon$-covering numbers for all $\varepsilon>0$?
Let $(E, d)$ be a metric space. For $\varepsilon>0$, we define two notions of $\varepsilon$-covering number as follows, i.e.,
$N_\varepsilon^o (E)$ is the smallest number of open balls whose radii ...
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