The continuity of the metric projection on a~subspace of finite codimension in the space of continuous functions
Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 531-539
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The closed subspaces of finite codimension of the space $C(X)$ of all continuous real-valued functions on a compact Hausdorff space $X$, for which the set of elements of best approximations of every function $f\in C(X)$ is nonempty and compact, are characterized. It is shown that if the compact Hausdorff space $X$ is infinite, then $C(X)$ has no subspace of a finite Codimension $n>1$ which has a nonempty set of elements of the best approximation for an arbitrary function $f\in C(X)$ and which has an upper-semicontinuous metric projection.
@article{MZM_1976_19_4_a5,
author = {E. V. Oshman},
title = {The continuity of the metric projection on a~subspace of finite codimension in the space of continuous functions},
journal = {Matemati\v{c}eskie zametki},
pages = {531--539},
publisher = {mathdoc},
volume = {19},
number = {4},
year = {1976},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a5/}
}
TY - JOUR AU - E. V. Oshman TI - The continuity of the metric projection on a~subspace of finite codimension in the space of continuous functions JO - Matematičeskie zametki PY - 1976 SP - 531 EP - 539 VL - 19 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a5/ LA - ru ID - MZM_1976_19_4_a5 ER -
E. V. Oshman. The continuity of the metric projection on a~subspace of finite codimension in the space of continuous functions. Matematičeskie zametki, Tome 19 (1976) no. 4, pp. 531-539. http://geodesic.mathdoc.fr/item/MZM_1976_19_4_a5/