Abstract
A compact space Q similar to the compact space known as Alexandroff's double arrow space is constructed. It is shown that the real space C(Q) has no Chebyshev subspaces of codimension >1, but the complex space C(Q) has such subspaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
.R. R. Phelps, “Čebyšev subspaces of finite codimension in C(X),” Pacific J. Math., 13 (1963), no. 2, 647-655.
A. L. Garkavi, “The Helly problem and best approximation in the space of continuous functions,” Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.], 31 (1967), no. 3, 641-656.
A. L. Garkavi, “On compact spaces admitting Chebyshev systems of measures,” Mat. Sb. [Math. USSR-Sb.], 74 (116) (1967), no. 2, 209-217.
A. L. Brown, “Chebyshev subspaces of finite codimension in spaces of continuous functions,” J. Austral. Math. Soc. Ser. A, 26 (1978), no. 1, 99-109.
L. P. Vlasov, “Approximative properties of subspaces of finite codimension in C(Q),” Mat. Zametki [Math. Notes], 28 (1980), no. 2, 205-222.
L. P. Vlasov, “The existence of elements of best approximation in a complex C(Q),” Mat. Zametki [Math. Notes], 40 (1986), no. 5, 627-634.
L. P. Vlasov, “Chebyshev subspaces of finite codimension in a complex C(Q),” Mat. Zametki [Math. Notes], 62 (1997), no. 2, 178-191.
N. Dunford and J. T. Schwartz, Linear Operators. General Theory, New York, Interscience, 1958.
J. L. Kelley, General Topology, Toronto-London-New York, D. Van Nostrand Company, 1957.
V. V. Fedorchuk, “On compact spaces with noncoinciding dimensions,” Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.], 182 (1968), no. 2, 275-277.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Vlasov, L.P. Alexandroff's Double Arrow Compact Space and Approximation Theory. Mathematical Notes 69, 749–755 (2001). https://doi.org/10.1023/A:1010222229776
Issue Date:
DOI: https://doi.org/10.1023/A:1010222229776