Semimetric space | Wikipedia audio article
Channel: wikipedia tts
Date: 28/03/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Metric_(mathematics)


00:00:42 1 Definition
00:02:55 2 Notes
00:03:30 3 Examples
00:03:41 4 Equivalence of metrics
00:06:55 5 Metrics on vector spaces
00:07:50 6 Metrics on multisets
00:09:46 7 Generalized metrics
00:13:30 7.1 Extended metrics
00:14:05 7.2 Pseudometrics
00:14:45 7.3 Quasimetrics
00:15:20 7.4 Metametrics
00:15:48 7.5 Semimetrics
00:16:17 7.6 Premetrics
00:16:42 7.7 Pseudoquasimetrics
00:18:11 7.8 Important cases of generalized metrics
00:18:17 8 See also
00:18:41 9 Notes
00:19:10 10 References
00:19:22 11 External links
00:19:44 0   if and only if   x
00:20:47 Premetrics
00:21:48 { x | d(x, A)
00:22:00 Pseudoquasimetrics
00:22:35 1 and d(1,0)
00:23:31 Important cases of generalized metrics
00:24:42 See also



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SUMMARY
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In mathematics, a metric or distance function is a function that defines a distance  between each pair of elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set, but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.
An important source of metrics in differential geometry are metric tensors, bilinear forms that may be defined from the tangent vectors of a differentiable manifold onto a scalar. A metric tensor allows distances along curves to be determined through integration, and thus determines a metric. However, not every metric comes from a metric tensor in this way.