Pseudometric Space - Examples

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.

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