- mathematics, a
pseudometric space is a
generalization of a
metric space in
which the
distance between two
distinct points can be zero.
Pseudometric spaces were...
-
Pseudometric may
refer to: The
metric of a pseudo-Riemannian manifold, a non-degenerate, smooth,
symmetric tensor field of
arbitrary signature Pseudometric...
- x\rVert :=d(x,0).} A
similar relationship holds between seminorms and
pseudometrics.
Among examples of
metrics induced by a norm are the
metrics d1, d2...
-
mathematics and
especially complex geometry, the
Kobayashi metric is a
pseudometric intrinsically ****ociated to any
complex manifold. It was
introduced by...
-
limit exists because the real
numbers are complete.) This is only a
pseudometric, not yet a metric,
since two
different Cauchy sequences may have the...
-
equivalently using systems of
pseudometrics, an
approach that is
particularly useful in
functional analysis (with
pseudometrics provided by seminorms). More...
- by a
metric (resp.
pseudometric). An LM-space is an
inductive limit of a
sequence of
locally convex metrizable TVS. A
pseudometric on a set X {\displaystyle...
- continuum). A
separable measure space has a
natural pseudometric that
renders it
separable as a
pseudometric space. The
distance between two sets is defined...
- the seminorm-induced topology, via the
canonical translation-invariant
pseudometric d p : X × X → R {\displaystyle d_{p}:X\times X\to \mathbb {R} } ; d p...
-
useful than
others depending on the application. (BCT1)
Every complete pseudometric space is a
Baire space. In particular,
every completely metrizable topological...
