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Let $X$ be a compact metric space and $K(X)$ is the set of closed subsets of $X$. That is, (K(X),dH)(K(X),dH) is also compact metric space. where $d_H$ is hausdorff metric. If $X$ acr, then $B:[0,1]\times X\to K(X)$ is not continuous. " Let $\mathcal{C}$ is circular arc.

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I do not understand why it is discontinuous. I want to know the detailed explanation. please help me.

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    Can you compute the Hausdorff distance between two $B(x,r)$'s? – 2017-02-06
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    yes, I can. $d_H(C,D)=\max\{\sup_{c\in C}\inf_{d\in D}d(c,d), \sup_{d\in D}\inf_{c\in C}d(c,d)\}$ where $C, D= closed ball $ – 2017-02-07
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    Henno Brandsma, I wait your explanation. – 2017-02-07
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    If possible, I would appreciate it if you could explain the problem. – 2017-02-07
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    Who says I can? I'm just interested. Did you check books, like Nadler's book on hyperspaces? – 2017-02-07
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    I just know that $K(X)$ is an intersting object. I haven't looked at metric properties of those a lot, just general topological notions. – 2017-02-07
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    E.g. go to the library and look at https://books.google.nl/books/about/Hyperspaces.html?id=TWo2h710HysC&redir_esc=y – 2017-02-07

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