Notes on Pointed Gromov-Hausdorff Convergence

TL;DR

This paper provides an introduction and investigation into pointed Gromov-Hausdorff convergence, exploring its properties, sublimits, and relation to ultralimits for both compact and pointed metric spaces.

Contribution

It offers a comprehensive overview of pointed Gromov-Hausdorff convergence, including new insights into sublimits and ultralimits within this framework.

Findings

Analysis of sublimits in pointed Gromov-Hausdorff convergence

Discussion of the relation between sublimits and ultralimits

Extension of convergence concepts to both compact and pointed metric spaces

Abstract

The present article addresses to everyone who starts working with (pointed) Gromov-Hausdorff convergence. In the major part, both Gromov-Hausdorff convergence of compact and of pointed metric spaces are introduced and investigated. Moreover, the relation of sublimits occurring with pointed Gromov-Hausdorff convergence and ultralimits is discussed.