Abstract
In this chapter we fix some conventions and recall the main definitions. The chapter may be used as a quick reference when reading the book. To learn background in metric geometry, the reader may consult the book of Dmitri Burago, Yuri Burago, and Sergei Ivanov [20].
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Notes
- 1.
Various authors call it differently: shortest path, minimizing geodesic.
- 2.
Note that while this notation slightly conflicts with the previously defined notation for distance on a general metric space, we will usually work with ambient length spaces where the meaning will be unambiguous.
- 3.
Formally speaking, convergence is the topology induced by \(\uprho \) on \(\varvec{X}\).
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Alexander, S., Kapovitch, V., Petrunin, A. (2019). Preliminaries. In: An Invitation to Alexandrov Geometry. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-05312-3_1
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DOI: https://doi.org/10.1007/978-3-030-05312-3_1
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