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The term antonym (and the related antonymy) is commonly taken to be synonymous with opposite, but antonym also has other more restricted meanings. Graded (or gradable) antonyms are word pairs whose meanings are opposite and which lie on a continuous spectrum (hot, cold).
The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based on the analogy that, in the case of metric spaces, (n + 1)-dimensional balls have n-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries of open sets. Moreover ...
Dimension (vector space), a property of vector spaces; Bipartite dimension, an intrinsic property of undirected graphs; Fractal dimension, a property of fractals; Global dimension, a homological property of mathematical rings; Krull dimension, an ideal property of mathematical rings; Order dimension, a property of partially ordered sets
Though long used informally, this term has found a formal definition in category theory. pathological An object behaves pathologically (or, somewhat more broadly used, in a degenerated way) if it either fails to conform to the generic behavior of such objects, fails to satisfy certain context-dependent regularity properties, or simply disobeys ...
In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several inequivalent notions of assigning a dimension to a given topological space. [1] A graphical illustration of a zero-dimensional space is a point. [2]
The dimension of a linear space is defined as the maximal number of linearly independent vectors or, equivalently, as the minimal number of vectors that span the space; it may be finite or infinite. Two linear spaces over the same field are isomorphic if and only if they are of the same dimension.
Definition: [7] The midpoint of two elements x and y in a vector space is the vector 1 / 2 (x + y). Theorem [ 7 ] [ 8 ] — Let A : X → Y be a surjective isometry between normed spaces that maps 0 to 0 ( Stefan Banach called such maps rotations ) where note that A is not assumed to be a linear isometry.
In the folding model, hyperspace is a place of higher dimension through which the shape of our three-dimensional space can be distorted to bring distant points close to each other; a common analogy popularized by Robert A. Heinlein's Starman Jones (1953) is that of crumpling two-dimensional paper or cloth in the third dimension, thus bringing ...