Geodesic
Uniform Continuity of Generalized Rational Approximations
Matematičeskie zametki, Tome 71 (2002) no. 2, pp. 261-270.

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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 $\varepsilon$. 
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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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