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Izv. RAN. Ser. Mat., 2018, Volume 82, Issue 4, Pages 199–224 (Mi izv8695)  

Continuous selections for metric projection operators and for their generalizations

I. G. Tsar'kov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: 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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00295-a
This paper was written with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00295-a).


DOI: https://doi.org/10.4213/im8695

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English version:
Izvestiya: Mathematics, 2018, 82:4, 837–859

Bibliographic databases:

UDC: 517.982.256
MSC: 54C65, 46B20, 54E25
Received: 27.05.2017

Citation: I. G. Tsar'kov, “Continuous selections for metric projection operators and for their generalizations”, Izv. RAN. Ser. Mat., 82:4 (2018), 199–224; Izv. Math., 82:4 (2018), 837–859

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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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