Geodesic
Spaces with a~uniformly continuous metric projection
Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 3-12.

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This paper contains a characterization of spaces in which the metric projection is uniformly continuous on the class of convex existence sets. 
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     author = {V. I. Berdyshev},
     title = {Spaces with a~uniformly continuous metric projection},
     journal = {Matemati\v{c}eskie zametki},
     pages = {3--12},
     publisher = {mathdoc},
     volume = {17},
     number = {1},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a0/}
}
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V. I. Berdyshev. Spaces with a~uniformly continuous metric projection. Matematičeskie zametki, Tome 17 (1975) no. 1, pp. 3-12. http://geodesic.mathdoc.fr/item/MZM_1975_17_1_a0/