TY - JOUR
T1 - Existence of chebyshev centers, best //-nets and best compact approximants
AU - Amir, Dan
AU - Mach, Jaroslav
AU - Saatkamp, Klaus
PY - 1982/6
Y1 - 1982/6
N2 - In this paper we investigate the existence and continuity of Chebyshev centers, best «-nets and best compact sets. Some of our positive results were obtained using the concept of quasi-uniform convexity. Furthermore, several examples of nonexistence are given, e.g., a sublattice M of C[0, 1], and a bounded subset B C M is constructed which has no Chebyshev center, no best n-net and not best compact set approximant.
AB - In this paper we investigate the existence and continuity of Chebyshev centers, best «-nets and best compact sets. Some of our positive results were obtained using the concept of quasi-uniform convexity. Furthermore, several examples of nonexistence are given, e.g., a sublattice M of C[0, 1], and a bounded subset B C M is constructed which has no Chebyshev center, no best n-net and not best compact set approximant.
UR - http://www.scopus.com/inward/record.url?scp=0013429919&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1982-0654848-2
DO - 10.1090/S0002-9947-1982-0654848-2
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AN - SCOPUS:0013429919
SN - 0002-9947
VL - 271
SP - 513
EP - 524
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 2
ER -