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Post Closed as "Not suitable for this site" by R W, Jan-Christoph Schlage-Puchta, András Bátkai, Franz Lemmermeyer, Alex Degtyarev
typo fixed
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András Bátkai
András Bátkai
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Let $(X,d)$ be a non-empty complete metric space, let M be the set of all non-empty compact subsets equipped with the Hausdorff metric, and $N$ be a positive integer. Is $$ \{A\subset X : 1\le \# X \le N \} $$$$ \{A\subset X : 1\le \# A \le N \} $$ a closed subset of $M$?

Let $(X,d)$ be a non-empty complete metric space, let M be the set of all non-empty compact subsets equipped with the Hausdorff metric, and $N$ be a positive integer. Is $$ \{A\subset X : 1\le \# X \le N \} $$ a closed subset of $M$?

Let $(X,d)$ be a non-empty complete metric space, let M be the set of all non-empty compact subsets equipped with the Hausdorff metric, and $N$ be a positive integer. Is $$ \{A\subset X : 1\le \# A \le N \} $$ a closed subset of $M$?

added top-level tag; http://meta.mathoverflow.net/questions/1457/why-are-mo-tags-formatted-as-they-are
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edit approved Jun 23, 2016 at 16:21
Martin Sleziak
edit approved Jun 23, 2016 at 16:21
Martin Sleziak
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Is the following set closed with respect to the hausdorffHausdorff metric?

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Martinus Maximus
Martinus Maximus
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Is the following set closed with respect to the hausdorff metric?

Let $(X,d)$ be a non-empty complete metric space, let M be the set of all non-empty compact subsets equipped with the Hausdorff metric, and $N$ be a positive integer. Is $$ \{A\subset X : 1\le \# X \le N \} $$ a closed subset of $M$?