-
equivalently using systems of
pseudometrics, an
approach that is
particularly useful in
functional analysis (with
pseudometrics provided by seminorms). More...
-
Pseudometric may
refer to: The
metric of a pseudo-Riemannian manifold, a non-degenerate, smooth,
symmetric tensor field of
arbitrary signature Pseudometric...
- a
topology is
generated using a
family of
pseudometrics, the
space is
called a
gauge space. A
pseudometric space ( X , d ) {\displaystyle (X,d)} is a...
- 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...
-
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...
-
induced by a
family of
pseudometrics; indeed, this is
because any
uniformity on a set X can be
defined by a
family of
pseudometrics.
Showing that a space...
- 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...
-
because they lack one or more
properties of
proper metrics. For example,
pseudometrics violate property (2),
identity of indiscernibles;
quasimetrics violate...
-
uniform space, or
equivalently the
topology being defined by a
family of
pseudometrics Simon, Jonathan. "Metrization Theorems" (PDF).
Retrieved 16 June 2016...
- 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...
