Tight Span

(Metric Geometry)

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Metric Geometry
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What is Tight span?

In metric geometry, the metric envelope or tight span of a metric space M is an injective metric space into which M can be embedded. In some sense it consists of all points "between" the points of M, analogous to the convex hull of a point set in a Euclidean space. The tight span is also sometimes known as the injective envelope or hyperconvex hull of M. It has also been called the injective hull, but should not be confused with the injective hull of a module in algebra, a concept with a similar description relative to the category of R-modules rather than metric spaces. The tight span was first described by , and it was studied and applied by in the 1960s. It was later independently rediscovered by and ; see for this history. The tight span is one of the central constructions of T-theory.

Technology Types

metric geometry

Synonyms

Hyperconvex hull

Translations

Инъективная оболочка (ru)

Tech Info


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