# Boundary of polyhedral spaces: an alternative proof.

Extracta Mathematicae (2000)

• Volume: 15, Issue: 1, page 213-217
• ISSN: 0213-8743

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## Abstract

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A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space (Theorem 1) and a related Theorem 2.

## How to cite

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Vesely, Libor. "Boundary of polyhedral spaces: an alternative proof.." Extracta Mathematicae 15.1 (2000): 213-217. <http://eudml.org/doc/38626>.

@article{Vesely2000,
abstract = {A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space (Theorem 1) and a related Theorem 2.},
author = {Vesely, Libor},
journal = {Extracta Mathematicae},
keywords = {Espacios de Banach; Poliedro compacto; polytope; density character; true face; boundary; polyhedral Banach space},
language = {eng},
number = {1},
pages = {213-217},
title = {Boundary of polyhedral spaces: an alternative proof.},
url = {http://eudml.org/doc/38626},
volume = {15},
year = {2000},
}

TY - JOUR
AU - Vesely, Libor
TI - Boundary of polyhedral spaces: an alternative proof.
JO - Extracta Mathematicae
PY - 2000
VL - 15
IS - 1
SP - 213
EP - 217
AB - A Banach space X is called polyhedral if the unit ball of each one of its finite-dimensional (equivalently: two-dimensional [6]) subspaces is a polytope. Polyhedral spaces were studied by various authors; most of the structural results are due to V. Fonf. We refer the reader to the surveys [1], [2] for other definitions of polyhedrality, main properties and bibliography. In this paper we present a short alternative proof of the basic result on the structure of the unit ball of the polyhedral space (Theorem 1) and a related Theorem 2.
LA - eng
KW - Espacios de Banach; Poliedro compacto; polytope; density character; true face; boundary; polyhedral Banach space
UR - http://eudml.org/doc/38626
ER -

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