# Infinite-dimensional sets of constant width and their applications.

Extracta Mathematicae (1990)

• Volume: 5, Issue: 2, page 41-52
• ISSN: 0213-8743

top

## Abstract

top
Sets of constant width appear as a curiosity in the context of finite-dimensional Euclidean spaces. These sets are convex bodies of such an space with the property that the distance between any two distinct parallel supporting hyperplanes is constant. The easiest example of a set of constant width which is not a ball is the so called Reuleaux triangle in the Euclidean plane. This is the intersection of three closed discs of radius r, whose centers are the vertices of an equilateral triangle of side length r.The aim of this talk is to show how, once finite-dimensional Euclidean spaces are replaced by arbitrary Banach spaces, the resulting concept of set of constant width becomes interesting in relation with several questions on the geometry of Banach spaces, mainly in what concerns the L-M theory.

## How to cite

top

Rodríguez Palacios, Angel. "Infinite-dimensional sets of constant width and their applications.." Extracta Mathematicae 5.2 (1990): 41-52. <http://eudml.org/doc/39866>.

@article{RodríguezPalacios1990,
abstract = {Sets of constant width appear as a curiosity in the context of finite-dimensional Euclidean spaces. These sets are convex bodies of such an space with the property that the distance between any two distinct parallel supporting hyperplanes is constant. The easiest example of a set of constant width which is not a ball is the so called Reuleaux triangle in the Euclidean plane. This is the intersection of three closed discs of radius r, whose centers are the vertices of an equilateral triangle of side length r.The aim of this talk is to show how, once finite-dimensional Euclidean spaces are replaced by arbitrary Banach spaces, the resulting concept of set of constant width becomes interesting in relation with several questions on the geometry of Banach spaces, mainly in what concerns the L-M theory.},
author = {Rodríguez Palacios, Angel},
journal = {Extracta Mathematicae},
language = {eng},
number = {2},
pages = {41-52},
title = {Infinite-dimensional sets of constant width and their applications.},
url = {http://eudml.org/doc/39866},
volume = {5},
year = {1990},
}

TY - JOUR
AU - Rodríguez Palacios, Angel
TI - Infinite-dimensional sets of constant width and their applications.
JO - Extracta Mathematicae
PY - 1990
VL - 5
IS - 2
SP - 41
EP - 52
AB - Sets of constant width appear as a curiosity in the context of finite-dimensional Euclidean spaces. These sets are convex bodies of such an space with the property that the distance between any two distinct parallel supporting hyperplanes is constant. The easiest example of a set of constant width which is not a ball is the so called Reuleaux triangle in the Euclidean plane. This is the intersection of three closed discs of radius r, whose centers are the vertices of an equilateral triangle of side length r.The aim of this talk is to show how, once finite-dimensional Euclidean spaces are replaced by arbitrary Banach spaces, the resulting concept of set of constant width becomes interesting in relation with several questions on the geometry of Banach spaces, mainly in what concerns the L-M theory.
LA - eng
UR - http://eudml.org/doc/39866
ER -

## NotesEmbed?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.