Geodesic
Continuous selections for metric projection operators and for their generalizations
Izvestiya. Mathematics , Tome 82 (2018) no. 4, pp. 837-859

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We study conditions on sets in asymmetric spaces under which there are continuous $\varepsilon$-selections or continuous selections for the metric projection. In particular, we give an affirmative answer to Brown's question on the existence of continuous selections for lower semicontinuous metric projections in polyhedral spaces.
Keywords: metric projection, continuous $\varepsilon$-selection, asymmetric spaces, polyhedral spaces. 
@article{IM2_2018_82_4_a5,
     author = {I. G. Tsar'kov},
     title = {Continuous selections for metric projection operators and for their generalizations},
     journal = {Izvestiya. Mathematics },
     pages = {837--859},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2018_82_4_a5/}
}
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I. G. Tsar'kov. Continuous selections for metric projection operators and for their generalizations. Izvestiya. Mathematics , Tome 82 (2018) no. 4, pp. 837-859. http://geodesic.mathdoc.fr/item/IM2_2018_82_4_a5/