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
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)