In mathematics, a zero-dimensional topological space (or nildimensional space) is a topological space that has dimension zero with respect to one of several...

Any straight line or smooth curve is a one-dimensional space, regardless of the dimension of the ambient space in which the line or curve is embedded. Examples...

case of metric spaces, (n + 1)-dimensional balls have n-dimensional boundaries, permitting an inductive definition based on the dimension of the boundaries...

0P (zero P) or 0-P may refer to: -polytope, a geometric form; see Zero-dimensional space 0-point energy or zero-point energy, the lowest possible energy...

0D (zero D) or 0-D may refer to: OD, IATA code for Darwin Airline Zero-day attack Zero-dimensional space 0x0D, the hex representation of newlines on some...

A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described...

finite-dimensional if the dimension of V {\displaystyle V} is finite, and infinite-dimensional if its dimension is infinite. The dimension of the vector space V {\displaystyle...

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible...

five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space. If...

every zero-dimensional vector space. If all zero-dimensional vector spaces are assigned this orientation, then, because all isomorphisms among zero-dimensional...

three-dimensional Euclidean space, that is, the Euclidean space of dimension three, which models physical space. More general three-dimensional spaces are...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space...

vector space. Any non-zero element of F serves as a basis so F is a 1-dimensional vector space over itself. The field is a rather special vector space; in...

in n-dimensional space. When n = 8, the set of all such locations is called 8-dimensional space. Often such spaces are studied as vector spaces, without...

indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist; conversely, a...

covered) and continuously, so that a one-dimensional object completely fills up a higher-dimensional object. Every space-filling curve hits some points multiple...

Six-dimensional space is any space that has six dimensions, six degrees of freedom, and that needs six pieces of data, or coordinates, to specify a location...

also refer to a seven-dimensional manifold such as a 7-sphere, or a variety of other geometric constructions. Seven-dimensional spaces have a number of special...

plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line...

plane is a flat two-dimensional surface that extends indefinitely. Euclidean planes often arise as subspaces of three-dimensional space R 3 {\displaystyle...

projective space of dimension n ≥ 3 is isomorphic with a PG(n, K), the n-dimensional projective space over some division ring K. A finite projective space is...

whose dimension is one less than that of the ambient space. Two lower-dimensional examples of hyperplanes are one-dimensional lines in a plane and zero-dimensional...

normal spaces. A zero-dimensional space with respect to the small inductive dimension has a base consisting of clopen sets. Every such space is regular...

real world four-dimensional space geometrically by projecting that space into a five-dimensional superspace with the fifth dimension corresponding to...

trivial action. As a vector space (over a field R), the zero vector space, zero-dimensional vector space or just zero space. These objects are described...

Euclidean space of dimension n, En (Euclidean line, E; Euclidean plane, E2; Euclidean three-dimensional space, E3) form a real coordinate space of dimension n...

in the space without any size or shape: zero-dimensional. Through any pair of points an infinite straight line can be drawn, a one-dimensional set of...

vectors define a three-dimensional space. The vectors o → {\displaystyle {\vec {o}}} (null vector, whose components are equal to zero) and k → {\displaystyle...

vector space is a finite-dimensional real or complex one, all norms are equivalent. On the other hand, in the case of infinite-dimensional vector spaces, not...

dimension is an infinite cardinal. Finite-dimensional vector spaces occur naturally in geometry and related areas. Infinite-dimensional vector spaces...