Discrete space information

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...

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

geometry Discrete geometry Continuous series representation Discrete series representation Discretization Interpolation Discrete measure Discrete space Ali...

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...

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

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...

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...

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...

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

intersections, the property of being an Alexandrov-discrete space is preserved under quotients. Alexandrov-discrete spaces are named after the Russian topologist...

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

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...

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...

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,...

{\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}...

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

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

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...

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...

scale space deals with continuous images, whereas one when implementing this theory will have to face the fact that most measurement data are discrete. Hence...

{\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...

energy minimization. In two dimensions, the active shape model represents a discrete version of this approach, taking advantage of the point distribution model...

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...

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...

neighborhood homeomorphic to Rn. The real coordinate space Rn is an n-manifold. Any discrete space is a 0-dimensional manifold. A circle is a compact 1-manifold...

concept is less important; it is anyway the case of a pointed discrete space. Pointed spaces are often taken as a special case of the relative topology,...

the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples...