Abstract
There are many ways to obtain new distances (metrics) from given distances (metrics). Metric transforms give new distances as a functions of given metrics (or given distances) on the same set X. A metric so obtained is called a transform metric. We give some important examples of transform metrics in Sect. 4.1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Burago D., Burago Y. and Ivanov S. A Course in Metric Geometry, Amer. Math. Soc., Graduate Studies in Math., Vol. 33, 2001.
Busemann H. The Geometry of Geodesics, Academic Press, New York, 1955.
Cameron P.J. and Tarzi S. Limits of cubes, Topology and its Appl., Vol. 155, pp. 1454–1461, 2008.
Corazza P. Introduction to metric-preserving functions, Amer. Math. Monthly, Vo. 104, pp. 309–323, 1999.
Deza M.M. and Laurent M. Geometry of Cuts and Metrics, Springer, 1997.
Foertsch T. and Schroeder V. Hyperbolicity, CAT( − 1)-spaces and the Ptolemy Inequality, Math. Ann., Vol. 350, pp. 339–356, 2011.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Deza, M.M., Deza, E. (2016). Metric Transforms. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52844-0_4
Download citation
DOI: https://doi.org/10.1007/978-3-662-52844-0_4
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-52843-3
Online ISBN: 978-3-662-52844-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)