In topology, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points form a discontinuous...

topology, a branch of mathematics, a discrete two-point space is the simplest example of a totally disconnected discrete space. The points can be denoted by...

preorder on the space. Spaces with an Alexandrov topology are also known as Alexandrov-discrete spaces or finitely generated spaces. The latter name...

isolated points is called a discrete set or discrete point set (see also discrete space). Any discrete subset S of Euclidean space must be countable, since...

Discrete modelling Discrete series representation Discrete space Discrete spectrum Discrete time and continuous time Discretization Interpolation Principal...

In computer science, a state space is a discrete space representing the set of all possible configurations of a system. It is a useful abstraction for...

group can be endowed with the discrete topology, making it a discrete topological group. Since every map from a discrete space is continuous, the topological...

{\displaystyle X.} In this case the topological space ( X , τ ) {\displaystyle (X,\tau )} is called a discrete space. Given X = Z , {\displaystyle X=\mathbb {Z}...

Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way analogous to discrete variables, having a bijection...

ground state, the continuous translational symmetry in space is broken and replaced by the lower discrete symmetry of the periodic crystal. As the laws of physics...

Discrete space, a simple example of a topological space Discrete spline interpolation, the discrete analog of ordinary spline interpolation Discrete time...

gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function...

space. The state space may be discrete or continuous, like the set of real numbers. A {\displaystyle A} is a set of actions called the action space (alternatively...

standard Borel space is the Borel space associated with a Polish space. Except in the case of discrete Polish spaces, the standard Borel space is unique,...

possible locations and therefore could not be continuous but must be discrete. Space could be thought of in a similar way to the relations between family...

arbitrarily many finite discrete spaces is a Stone space, and the topological space underlying any profinite group is a Stone space. The Stone–Čech compactification...

computations in scale-space theory, and for a complementary treatment regarding hybrid discretization methods. The Gaussian scale-space representation of...

Sierpiński space is compact. No discrete space with an infinite number of points is compact. The collection of all singletons of the space is an open...

to the property of being discrete (every set is open). Every discrete space is extremally disconnected. Every indiscrete space is both extremally disconnected...

Sequential spaces are CG-2. This includes first countable spaces, Alexandrov-discrete spaces, finite spaces. Every CG-3 space is a T1 space (because given...

frequency domain. A discrete frequency domain is a frequency domain that is discrete rather than continuous. For example, the discrete Fourier transform...

neighborhood U x {\displaystyle U_{x}} of x {\displaystyle x} and a discrete space D x {\displaystyle D_{x}} such that π − 1 ( U x ) = ⨆ d ∈ D x V d {\displaystyle...

applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This...

general: for instance Cantor space is totally disconnected but not discrete. Let X {\displaystyle X} be a topological space, and let x {\displaystyle x}...

and {a}. This topology is both discrete and trivial, although in some ways it is better to think of it as a discrete space since it shares more properties...

is closed as a subset of the product space X × X {\displaystyle X\times X} . Any injection from the discrete space with two points to X {\displaystyle...

cross-correlations. Discrete-space Fourier transform (DSFT) is the generalization of the DTFT from 1D signals to 2D signals. It is called "discrete-space" rather...

{\displaystyle n} -dimensional Euclidean space is separable. A simple example of a space that is not separable is a discrete space of uncountable cardinality. Further...

Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric...

there is no such index. This space is homeomorphic to the product of a countable number of copies of the discrete space S . {\displaystyle S.} Riemannian...