Geodesic
Uniform Continuity of Generalized Rational Approximations
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 261-270 
C. S. Rjutin. Uniform Continuity of Generalized Rational Approximations. Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 261-270. http://geodesic.mathdoc.fr/item/MZM_2002_71_2_a9/
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     title = {Uniform {Continuity} of {Generalized} {Rational} {Approximations}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, it is shown that there are no uniformly continuous multiplicative $\varepsilon$-selections from $C[0,1]$ on the set of generalized rational fractions of sufficiently general form for small $\varepsilon$.

[1] Konyagin S. V., “O nepreryvnosti operatorov obobschennogo ratsionalnogo priblizheniya”, Matem. zametki, 44:3 (1988), 404 | MR | Zbl

[2] Tsarkov I. G., “Svoistva mnozhestv, obladayuschikh nepreryvnoi vyborkoi iz operatora $P^\delta$”, Matem. zametki, 48:4 (1990), 122–131 | MR | Zbl

[3] Albrekht P. V., “Poryadki modulei nepreryvnosti operatorov pochti nailuchshego priblizheniya”, Matem. sb., 185:9 (1994), 3–28

[4] Marinov A. V., “Otsenki ustoichivosti nepreryvnoi selektsii dlya metricheskoi pochti-proektsii”, Matem. zametki, 55:4 (1994), 47–53 | MR | Zbl

[5] Konyagin S. V., “O ravnomernoi nepreryvnosti operatorov ratsionalnogo priblizheniya”, Teoriya priblizhenii i zadachi vychislitelnoi matematiki, Tezisy dokladov, Dnepropetrovsk, 1993, 108

[6] Ryutin K. S., “Lipshitsevost retraktsii i operator obobschennogo ratsionalnogo priblizheniya”, Fundament. i prikl. matem., 6:4 (2000), 1205–1220 | MR | Zbl