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Results tagged with mg.metric-geometry
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user 176409
Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
2
votes
2
answers
159
views
Monotonicity of doubling dimension
Let $(X,d)$ be a metric space with finite Assouad dimension $0<C_X$. It seems intuitive to me that if $\emptyset \subset Y\subseteq X$ then $Y$ is also doubling and its Assouad dimension, denoted her …
5
votes
1
answer
199
views
Criterion for Kuratowski Limit Inferior
Let $(X,d_X)$ be a compact metric space and let $\{K_n\}_{n=1}^{\infty}$ be a collection of non-empty compact subsets. Let $K\subseteq X$ be compact. Then, if for every $x_n \in K_n$ we have
$$
d_X( …
1
vote
0
answers
69
views
Injectivity of post-composition operator
Let $X$, $Y_1,Y_2$, and $Z$ be separable metric spaces. Let $C(X,Y)$ be the topological space of continuous functions from $X$ to $Y$ equipped with its compact-open topologies. Fix a continuous func …