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Generalizations of Metric Spaces

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Encyclopedia of Distances

Abstract

Some immediate generalizations of the notion of metric, for example, quasi-metric, near-metric, extended metric, were defined in Chap. 1. Here we give some generalizations in the direction of Topology, Probability, Algebra, etc.

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References

  1. Beer G. On Metric Boundedness Structures, Set-Valued Anal., Vol. 7, pp. 195–208, 1999.

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  2. Deza M.M. and Dutour M. Cones of Metrics, Hemi-metrics and Super-metrics, Ann. of European Academy of Sci., pp. 141–162, 2003.

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  3. Martin K. A Foundation for Computation, Ph.D. Thesis, Tulane University, Department of Mathematics, 2000.

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  4. Schweizer B. and Sklar A. Probabilistic Metric Spaces, North-Holland, Amsterdam, 1983.

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Deza, M.M., Deza, E. (2013). Generalizations of Metric Spaces. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30958-8_3

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