- injective envelope
- мат.инъективная оболочка
English-Russian scientific dictionary. 2008.
injective envelope
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Injective hull — This article is about the injective hull of a module in algebra. For injective hulls of metric spaces, also called tight spans, injective envelopes, or hyperconvex hulls, see tight span. In mathematics, especially in the area of abstract algebra… … Wikipedia
Injective cogenerator — In category theory, the concept of an injective cogenerator is drawn from examples such as Pontryagin duality. Generators are objects which cover other objects as an approximation, and (dually) cogenerators are objects which envelope other… … Wikipedia
Divisible group — In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive… … Wikipedia
Tight span — If a set of points in the plane, with the Manhattan metric, has a connected orthogonal convex hull, then that hull coincides with the tight span of the points. In metric geometry, the metric envelope or tight span of a metric space M is an… … Wikipedia
Projective cover — In category theory, a projective cover of an object X is in a sense the best approximation of X by a projective object P . Projective covers are the dual of injective envelopes. Definition Let mathcal{C} be a category and X an object in… … Wikipedia
Essential extension — In mathematics, specifically module theory, given a ring R and R modules :Msubseteq E, the module E is an essential extension if for every nonzero submodule :Nsubseteq E, we have:Ncap M e 0. Also, M is then said to be an essential submodule of E … Wikipedia
T-theory — is a branch of discrete mathematics dealing with analysis of trees and discrete metric spaces. General historyAs per Andreas Dress, T theory originated from a question raised by Manfred Eigen, a recipient of the Nobel Prize in Chemistry, in the… … Wikipedia
Category of metric spaces — The category Met, first considered by Isbell (1964), has metric spaces as objects and metric maps or short maps as morphisms. This is a category because the composition of two metric maps is again metric.The monomorphisms in Met are the injective … Wikipedia
Morphism — In mathematics, a morphism is an abstraction derived from structure preserving mappings between two mathematical structures. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear… … Wikipedia
Uniform space — In the mathematical field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and… … Wikipedia
Metric space aimed at its subspace — In mathematics, a metric space aimed at its subspace is a categorical construction that has a direct geometric meaning. It is also a useful step toward the construction of the metric envelope, or tight span, which are basic (injective) objects of … Wikipedia
