A 2-parameter Chebyshev set which is not a sun

Dunham, Charles B.

doi:10.1090/S0002-9939-1975-0402369-6

A $2$-parameter Chebyshev set which is not a sun
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by Charles B. Dunham PDF

Proc. Amer. Math. Soc. 50 (1975), 315-316 Request permission

Abstract:

Consider approximation with respect to the Chebyshev norm $||g|| = \sup \{ |g(x)|:0 \leq x \leq 1\}$ on $[0,1]$. A subset $G$ of $C[0,1]$ such that each $f \in C[0,1]$ has a unique best approximation from $G$ is called a Chebyshev set. It has been shown by the author that there exist Chebyshev sets which are not suns [2], but the examples given were essentially one-dimensional. An example is now given which is two-dimensional.

References

C. B. Dunham, Existence and continuity of the Chebyshev operator, SIAM Rev. 10 (1968), 444–446. MR 238011, DOI 10.1137/1010097

Chebyshev sets in $C[0,1]$ which are not suns

Günter Meinardus, Approximation of functions: Theory and numerical methods, Expanded translation of the German edition, Springer Tracts in Natural Philosophy, Vol. 13, Springer-Verlag New York, Inc., New York, 1967. Translated by Larry L. Schumaker. MR 0217482