Geodesic
An Example of Non-Approximatively-Compact Existence Set with Finite-Valued Metric Projection
Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 170-174

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An example indicated in the title is constructed in an arbitrary Banach lattice in which the order is defined by a countable symmetric Schauder basis with the symmetry constant 1 and which satisfies the additional condition of strict monotonicity of the norm with respect to the coordinates.
Keywords: Banach lattice, Hilbert space, symmetric Schauder basis, approximatively compact set, metric projection.
Mots-clés : existence set 
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     author = {P. A. Borodin and I. A. Pyatyshev},
     title = {An {Example} of {Non-Approximatively-Compact} {Existence} {Set} with {Finite-Valued} {Metric} {Projection}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {170--174},
     publisher = {mathdoc},
     volume = {86},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a1/}
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P. A. Borodin; I. A. Pyatyshev. An Example of Non-Approximatively-Compact Existence Set with Finite-Valued Metric Projection. Matematičeskie zametki, Tome 86 (2009) no. 2, pp. 170-174. http://geodesic.mathdoc.fr/item/MZM_2009_86_2_a1/