Hausdorff and Gromov distances in quantale-enriched categories.

摘要

This work studies Hausdorff and Gromov distances in quantale-enriched categories or V -categories. We study those distances from classical and categorical perspectives. The classical study is conducted in the category of metric spaces and its results are mostly well known, but even in this setting we relax standard assumptions in several theorems. The categorical approach builds on the results of the classical one. The latter approach led to the discovery of several interesting properties of those distances in a categorical setting. A concise introduction to V -categories is provided in the second chapter. The last chapter introduces the Vietoris topology and acts as a starting point for the treatment of this topology in a categorical setting.