Casacuberta, CarlesMartínez Vergara, Rafael2023-09-212023-09-212023-06-28https://hdl.handle.net/2445/202094Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Carles CasacubertaThis work provides an introduction to the Gromov-Hausdorff distance, discussing its original definition and its relationship with correspondences between spaces. We prove that the Gromov-Hausdorff distance serves as a metric for the set of isometry classes of compact metric spaces. The primary objectives of this study are to establish the existence of a pseudo-metric on the disjoint union $X \sqcup Y$ that achieves the Gromov-Hausdorff distance between compact spaces $X$ and $Y$, and to establish bounds for the Gromov-Hausdorff distance between spheres of different dimensions.55 p.application/pdfengcc by-nc-nd (c) Rafael Martínez Vergara, 2023http://creativecommons.org/licenses/by-nc-nd/3.0/es/Espais topològicsGeometria diferencialTreballs de fi de màsterTopological spacesDifferential geometryMaster's thesisinfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/openAccess