User maj - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T08:52:20Z http://mathoverflow.net/feeds/user/17472 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/74012/is-point-to-set-distance-continuous Is point to set distance continuous? Maj 2011-08-29T23:24:03Z 2011-08-30T00:43:42Z <p>Assume $\mathbf{d}:\mathbb{R}^n\times\mathbb{R}^n\rightarrow\mathbb{R}_0^+$ is a metric such that the function $\psi(x)=\mathbf{d}(x,y)$ for any $y\in\mathbb{R}^n$ is continuous in the Euclidean metric. Moreover, assume that $\mathcal{A}\subseteq\mathbb{R}^n$ is a closed set. My question: is $\phi(x)=\mathbf{d}(x,\mathcal{A})$ a continuous function in Euclidean metric? Note that $\mathbf{d}(x,\mathcal{A})$ is point to set distance. </p> http://mathoverflow.net/questions/74012/is-point-to-set-distance-continuous/74022#74022 Comment by Maj Maj 2011-08-30T18:25:27Z 2011-08-30T18:25:27Z Thanks Phil! Sorry if the question was silly.