# Questions tagged [hausdorff-distance]

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31 questions
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### Hausdorff metric and connectedness [duplicate]

Let $(X, d)$ be metric space. Define $B_\epsilon = \{ x \in X : \exists b \in B \; d(x, b) \le \epsilon\}$. Let $F(X)$ be a family of all nonempty compact subsets of $X$ (so $\emptyset \notin F(X)$ )....
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### Hausdorff distance between two set of finite points

Assume we have two (finite) sets of points, $A:=\{a_{1},\ldots,a_{n}\}$ and $B:=\{b_{1}, \ldots,b_{n}\}$ in the closed hypercube $[0,1]^{d}\subset \mathbb{R}^{d}$. Somebody know an "efficient" ...
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### Coordinates with KD tree?

So for my research, I need to find the "center" between two coordinates. In my instance, I have a neighborhood area, delimited by the coordinates of its angles which I will look up on google maps. ...
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### Bounds on the difference of sups in terms of the Hausdorff distance between feasible regions

Let $f: \mathbb{R}^{k} \mapsto \mathbb{R}$ be a bounded and continuous function, and suppose that $X \subset \mathbb{R}^{k}$ and $Y \subset \mathbb{R}^{k}$ are compact. I am reading a paper that ...
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### A sequence of affine images converges to an affine image

Take two sets $M,N\subset\mathbb{R}^n$, which I can assume to be compact and convex if required. If we have a sequence of affine functions $(T_n)$ such that $T_nM\to N$, I want to show that $N=TM$ ...
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### Locally compact hausdorff property.

$X$ is Hausdorff space. The following is equivalent. (a) $X$ is locally compact space. (b) For every open neighborhood $U$ of $x\in X$ there is a smaller open neighborhood $V$ of $x$ whose closure ...
Let $E = \mathbb{R}^N$ for some $N \in \mathbb{N}$ and $d(x,y)=||x-y||_2$ the euclidean distance. We note $K(E)$ the set of all compact sets of $E$, and we'll use the Hausdorff distance on $K(E)$ ...