Abstract
In this lecture, we remind several definitions related to metric spaces and fix some conventions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Others call it differently: shortest path, minimizing geodesic. Also, note that the meaning of the term geodesic is different from what is used in Riemannian geometry, altho they are closely related.
References
D. Burago, Yu. Burago, and S. Ivanov. A course in metric geometry. Vol. 33. Graduate Studies in Mathematics. 2001.
K. Menger. “Untersuchungen über allgemeine Metrik”. Math. Ann. 100.1 (1928), 75–163.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Petrunin, A. (2023). Definitions. In: Pure Metric Geometry. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-031-39162-0_1
Download citation
DOI: https://doi.org/10.1007/978-3-031-39162-0_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-39161-3
Online ISBN: 978-3-031-39162-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)