An introduction to the geometry of metric spaces
Stephen Semmes
TL;DR
This paper provides an accessible overview of fundamental properties of metric spaces, focusing on the concept of lengths of curves and their geometric implications.
Contribution
It introduces basic concepts and properties of metric spaces with an emphasis on the geometric aspect of curve lengths, serving as an educational resource.
Findings
Clarifies the relationship between metric space properties and curve lengths
Provides foundational understanding for further geometric analysis in metric spaces
Highlights key properties relevant to the study of metric geometry
Abstract
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
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Taxonomy
TopicsMathematics and Applications · Homotopy and Cohomology in Algebraic Topology · Advanced Differential Geometry Research