Examples
Pseudometrics arise naturally in functional analysis. Consider the space of real-valued functions together with a special point . This point then induces a pseudometric on the space of functions, given by
for
For vector spaces V, a seminorm p induces a pseudometric on V, as
Conversely, a homogeneous, translation invariant pseudometric induces a seminorm.
Pseudometrics also arise in the theory of hyperbolic complex manifolds: see Kobayashi metric.
Read more about this topic: Pseudometric Space
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