Let $X$ be a metric space and let $U,V\subset X$ be open and bounded subsets. Is the Hausdorff metric $$ h(U,V)=\max(\sup_{x\in U}\inf_{y\in V}d(x,y),\sup_{x\in V}\inf_{y\in U}d(x,y)) $$ defined for all possible choices of $U$ and $V$?
hausdorff metric between open and bounded sets
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functional-analysis
metric-spaces
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1Small typo, want $d(x,y)$ there. – 2012-09-02
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2Where do you see potential here for something not being defined? – 2012-09-02