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Results tagged with mg.metric-geometry
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user 114996
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
8
votes
1
answer
2k
views
Intersection of nested open ball in complete metric spaces is nonempty?
My question is that whether the following statement is true or not.
In a complete metric space $(X, d)$, if a sequence of open balls $\{B(x_i, r_i)\}_{i=1}^\infty$ satisfies
$$
\exists \epsilon > 0 ~ …
CommunityBot
- 1
2
votes
1
answer
138
views
Covering a circle with small balls centered at nodes on a tiling
In $\mathbb{R}$, we have $n$ finite sets, namely $\{A_1,A_2,\dots, A_n\}$. From them, we define a tiling:
$$
T := \{x\in \mathbb{R}^n: \forall i \in \{1,2,\dots,n\}, ~x_i\in A_i\} = \prod_{i=1}^nA_i
$ …
- 30.1k