Geodesic
On the radius of a compact set in Hilbert space
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 157-158

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In this note we improve the formula $r(A)\leq\frac{1}{\sqrt{2}}\delta(A)$ proved by Routledge for Hilbert spaces. We show that if $A$ is a relatively compact set, then $r(A)\leq\frac{1}{\sqrt{2}}\delta(A)$. 
@article{ZNSL_1988_167_a10,
     author = {N. M. Gulevich},
     title = {On the radius of a compact set in {Hilbert} space},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {157--158},
     publisher = {mathdoc},
     volume = {167},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a10/}
}
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N. M. Gulevich. On the radius of a compact set in Hilbert space. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part 6, Tome 167 (1988), pp. 157-158. http://geodesic.mathdoc.fr/item/ZNSL_1988_167_a10/