# name
On the Gromov-Hausdorff distance between compact spaces

# metadata.dc.description[].value
Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2022-2023. Director: Carles Casacuberta

# metadata.dc.description.abstract[].value
This 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.

# metadata.dc.rights[].value
cc by-nc-nd (c) Rafael Martínez Vergara, 2023

# metadata.dc.title[].value
On the Gromov-Hausdorff distance between compact spaces