Definition of Pseudometrics. Meaning of Pseudometrics. Synonyms of Pseudometrics

Here you will find one or more explanations in English for the word Pseudometrics. Also in the bottom left of the page several parts of wikipedia pages related to the word Pseudometrics and, of course, Pseudometrics synonyms and on the right images related to the word Pseudometrics.

Definition of Pseudometrics

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Meaning of Pseudometrics from wikipedia

- 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...
- because they lack one or more properties of proper metrics. For example, pseudometrics violate property (2), identity of indiscernibles; quasimetrics violate...
- 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...
- 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...
- complex spaces is distance-decreasing with respect to the Kobayashi pseudometrics of X and Y. It follows that if two points p and q in a complex space...