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Distance k-sectors exist

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F10%3A10038287" target="_blank" >RIV/00216208:11320/10:10038287 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Distance k-sectors exist

  • Original language description

    The bisector of two nonempty sets P and Q in a metric space is the set of all points with equal distance to P and to Q. A distance k-sector of P and Q, where k ? 2 is an integer, is a (k-1)-tuple (C1, C2, ..., Ck-1) such that Ci is the bisector of Ci-1 and Ci+1 for every i= 1, 2, ..., k-1, where C0 = P and Ck = Q. This notion, for the case where P and Q are points in Euclidean plane, was introduced by Asano, Matousek, and Tokuyama. They established the existence and uniqueness of the distance trisectorin this special case. We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension, or more generally, in proper geodesic spaces (uniqueness remains open).The core of the proof is a new notion of k-gradation for P and Q, whose existence (even in an arbitrary metric space) is proved using the Knaster-Tarski fixed point theorem, by a method introduced by Reem and Reich for a slightly differe

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

    BA - General mathematics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Others

  • Publication year

    2010

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    Proceedings of the 2010 annual symposium on Computational geometry

  • ISBN

    978-1-4503-0016-2

  • ISSN

  • e-ISSN

  • Number of pages

    6

  • Pages from-to

  • Publisher name

    Association for Computing Machinery

  • Place of publication

    Neuveden

  • Event location

    Snowbird, Utah

  • Event date

    Jun 13, 2010

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article

    000281594400027