The Gromov–Hausdorff distance between compact metric spaces

Authors

  • Rafael Martínez Vergara Universitat de Barcelona

Keywords:

Hausdorff, metric, correspondance

Abstract

Aquest treball proporciona una introducció a la distancia de Gromov–Hausdorff, discutim la seva definició original i la seva relació amb les correspondències entre espais. Demostrem que la distància de Gromov–Hausdorff serveix com a mètrica per al conjunt de classes d’isometria d’espais mètrics compactes. Els objectius principals d’aquest estudi són establir l’existència d’una pedomètrica en la unió disjunta de X amb Y que aconsegueix la distància de Gromov–Hausdorff entre espais compactes X i Y, i per establir límits per al Gromov–Hausdorff distància entre esferes de diferents dimensions.

Downloads

Download data is not yet available.

Downloads

Published

2024-01-26

How to Cite

Martínez Vergara, R. (2024). The Gromov–Hausdorff distance between compact metric spaces. Reports@SCM, 8(1), 59–60. Retrieved from https://revistes.iec.cat/index.php/reports/article/view/151069

Issue

Vol. 8 No. 1 (2023)

Section

Extended Abstracts

License

The intellectual property of articles belongs to the respective authors.
On submitting articles for publication to the journal Reports@SCM, authors accept the following terms:
  1. Authors assign to Societat Catalana de Matemàtiques (a subsidiary of Institut d’Estudis Catalans) the rights of reproduction, communication to the public and distribution of the articles submitted for publication to Reports@SCM.
  2. Authors answer to Societat Catalana de Matemàtiques for the authorship and originality of submitted articles.
  3. Authors are responsible for obtaining permission for the reproduction of all graphic material included in articles.
  4. Societat Catalana de Matemàtiques declines all liability for the possible infringement of intellectual property rights by authors.
  5. The contents published in the journal, unless otherwise stated in the text or in the graphic material, are subject to a Creative Commons Attribution-NonCommercial-NoDerivs (by-nc-nd) 3.0 Spain licence, the complete text of which may be found at https://creativecommons.org/licenses/by-nc-nd/3.0/es/deed.en. Consequently, the general public is authorised to reproduce, distribute and communicate the work, provided that its authorship and the body publishing it are acknowledged, and that no commercial use and no derivative works are made of it.
  6. The journal Reports@SCM is not responsible for the ideas and opinions expressed by the authors of the published articles.