Fundamental sets of continuous functions on spheres |
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| Authors: | Xingping Sun E. W. Cheney |
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| Affiliation: | 1. Department of Mathematics, Southwest Missouri State University, 65804, Springfield, MO, USA
2. Department of Mathematics, University of Texas-Austin and University of Leicester, 78712-1082, Austin, TX, USA
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| 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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