Nonexistence of continuous selections of the metric projection for a class of weak Chebyshev spaces

Author:
Manfred Sommer

Journal:
Trans. Amer. Math. Soc. **260** (1980), 403-409

MSC:
Primary 41A65; Secondary 41A50, 41A52

DOI:
https://doi.org/10.1090/S0002-9947-1980-0574787-3

MathSciNet review:
574787

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Abstract: The class of all those *n*-dimensional weak Chebyshev subspaces of whose elements have no zero intervals is considered. It is shown that there does not exist any continuous selection of the metric projection for *G* if there is a nonzero *g* in *G* having at least distinct zeros. Together with a recent result of Nürnberger-Sommer, the following characterization of continuous selections for is valid: There exists a continuous selection of the metric projection for *G* in if and only if each nonzero *g* in *G* has at most *n* distinct zeros.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1980-0574787-3

Keywords:
Continuous selection,
metric projection,
weak Chebyshev spaces

Article copyright:
© Copyright 1980
American Mathematical Society