Metric

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Metric
d:X×XR0
Where X is any set
relation to other topological spaces
is a
contains all
Related objects
Induced by norm
  • d:V×VR0
  • d:(x,y)xy

For V a vector space over R or C

Induced by inner product

An inner product induces a norm:

  • ,:VR0
  • ,:xx,x

Which induces a metric:

  • d,:V×VR0
  • d,:(x,y)xy,xy
A metric is the most abstract notion of distance. It requires no structure on the underlying set.

Contents

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Definition


TODO: Separate metric and metric space