specifically in order theory and functional analysis, an abstract m-space or an AM-space is a Banach lattice ( X , ‖ ⋅ ‖ ) {\displaystyle (X,\|\cdot...

usefulness of the word "abstract". The word applies to properties and relations to mark the fact that, if they exist, they do not exist in space or time, but that...

distinction: Spatiotemporal existence – Abstract objects exist outside space-time, while concrete objects exist within space-time. Causal influence – Concrete...

Abstract expressionism in the United States emerged as a distinct art movement in the aftermath of World War II and gained mainstream acceptance in the...

(1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5 Grillet, Pierre Antoine (2007), Abstract algebra, Graduate Texts in Mathematics...

include groups, rings, fields, modules, vector spaces, lattices, and algebras over a field. The term abstract algebra was coined in the early 20th century...

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric...

In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over...

\|u\|_{M}=\sup\{|\langle u,\mu \rangle |;\|\mu \|_{L}\leq 1\}} is called an abstract M-space. It's also a lattice with unit defined through I μ = ‖ μ + ‖ L − ‖...

Kakutani, Shizuo (1941). "Concrete representation of abstract (M)-spaces. (A characterization of the space of continuous functions.)". Ann. of Math. Series...

In computer science, an abstract data type (ADT) is a mathematical model for data types, defined by its behavior (semantics) from the point of view of...

: 25  A realization of an abstract polytope is a mapping of its vertices to points a geometric space (typically a Euclidean space).: 121  A faithful realization...

Abstract art uses visual language of shape, form, color and line to create a composition which may exist with a degree of independence from visual references...

admit the structure of a metric space, including Riemannian manifolds, normed vector spaces, and graphs. In abstract algebra, the p-adic numbers arise...

coined the term Hilbert space for the abstract concept that underlies many of these diverse applications. The success of Hilbert space methods ushered in a...

The column space of an m × n matrix with components from F {\displaystyle F} is a linear subspace of the m-space F m {\displaystyle F^{m}} . The dimension...

in Lagrangian or Hamiltonian mechanics; these are abstract spaces, independent of the physical space. In mathematics, the dimension of an object is, roughly...

said to be a realization of an abstract polytope in some real N-dimensional space, typically Euclidean. This abstract definition allows more general combinatorial...

In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node...

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates)...

2001: A Space Odyssey is a 1968 epic science fiction film produced and directed by Stanley Kubrick. The screenplay was written by Kubrick and Arthur C...

abstract (L)-spaces and the mean ergodic theorem." Annals of Mathematics (1941): 523–537. doi:10.2307/1968915 "Concrete representation of abstract (M)-spaces...

such spaces are open to all, while private property is the land culturally owned by an individual or company, for their own use and pleasure. Abstract space...

concept of a Projective space plays a central role in algebraic geometry. This article aims to define the notion in terms of abstract algebraic geometry and...

“abstract” since its points, which are called “cells”, are not subsets of a Hausdorff space as is the case in Euclidean and CW complexes. Abstract cell...

position space (their norm squared). The wave functions represent the abstract state characterized by the triple of quantum numbers (n, ℓ, m), in the...

mathematics, an inner product space (or, rarely, a Hausdorff pre-Hilbert space) is a real vector space or a complex vector space with an operation called an...

within a defined boundary (or surface), that exists in space and time. Usually contrasted with abstract objects and mental objects. Also in common usage, an...

quotient space is a vector space formed by taking a quotient group, where the quotient homomorphism is a linear map. By extension, in abstract algebra...

and the abstract state spaces are Galois connected. This means that if we take an element from the abstract space, concretize it and abstract the concretized...