-
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...
-
equivalently using systems of
pseudometrics, an
approach that is
particularly useful in
functional analysis (with
pseudometrics provided by seminorms). More...
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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...
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because they lack one or more
properties of
proper metrics. For example,
pseudometrics violate property (2),
identity of indiscernibles;
quasimetrics violate...
- 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...
- 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...
-
uniform space, or
equivalently the
topology being defined by a
family of
pseudometrics Simon, Jonathan. "Metrization Theorems" (PDF).
Retrieved 16 June 2016...
-
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...
- is a
sensible structure on X; it is a
pseudometric. (Again,
there is a more
direct definition of
pseudometric.) In this way,
there is a
natural way to...
