Elementary aspects of the geometry of metric spaces

TL;DR

This paper surveys fundamental geometric properties of metric spaces, highlighting their relevance to manifolds, norms, and fractal sets, and discusses key concepts and questions in the field.

Contribution

It provides an overview of elementary aspects of metric space geometry, connecting basic ideas to broader mathematical contexts.

Findings

Identifies core geometric features of metric spaces

Connects metric space concepts to manifolds and fractals

Summarizes key questions and ingredients in metric geometry

Abstract

The setting of metric spaces is very natural for numerous questions concerning manifolds, norms, and fractal sets, and a few of the main ingredients are surveyed here.