Abstract
LetS m andS ∞ denote the unit spheres inR m+1 ande 2, respectively. We look for functionsf inC[−1, 1] such that the family of functionsx →f(<s,v>) is fundamental in the spaceC(S m). Herev runs overS m. There is a similar question forC(S ∞), when this space is given the topology of uniform convergence on compact sets.
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Communicated by Tim Goodman.
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Sun, X., Cheney, E.W. Fundamental sets of continuous functions on spheres. Constr. Approx 13, 245–250 (1997). https://doi.org/10.1007/BF02678466
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DOI: https://doi.org/10.1007/BF02678466