Premetric space | Wikipedia audio article
Channel: wikipedia tts
Date: 18/02/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Metric_(mathematics)


00:00:56 1 Definition
00:03:51 2 Notes
00:04:37 3 Examples
00:04:48 4 Equivalence of metrics
00:09:02 5 Metrics on vector spaces
00:10:11 6 Metrics on multisets
00:12:43 7 Generalized metrics
00:17:34 7.1 Extended metrics
00:18:19 7.2 Pseudometrics
00:19:10 7.3 Quasimetrics
00:19:56 7.4 Metametrics
00:20:33 7.5 Semimetrics
00:21:10 7.6 Premetrics
00:21:42 7.7 Pseudoquasimetrics
00:23:40 7.8 Important cases of generalized metrics
00:23:48 8 See also
00:24:20 9 Notes
00:24:56 10 References
00:25:12 11 External links
00:25:41 0   if and only if   x
00:27:05 Premetrics
00:28:26 { x | d(x, A)
00:28:39 Pseudoquasimetrics
00:29:24 1 and d(1,0)
00:30:35 Important cases of generalized metrics
00:32:07 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.