In mathematics, especially in geometry and topology, an ambient space is the space surrounding a mathematical object along with the object itself. For...

modern mathematics uses many types of spaces, such as Euclidean spaces, linear spaces, topological spaces, Hilbert spaces, or probability spaces, it does...

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

of the ambient space), the condition means that the tangent space to the ambient manifold is the direct sum of the two smaller tangent spaces. If an intersection...

“size” (where the meaning of “size” depends on the structure of the ambient space). The term precompact (or pre-compact) is sometimes used with the same...

A one-dimensional space (1D space) is a mathematical space in which location can be specified with a single coordinate. An example is the number line,...

hypersurface, a subspace whose dimension is one less than that of the ambient space. Two lower-dimensional examples of hyperplanes are one-dimensional lines...

In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example...

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

In mathematics, a knot is an embedding of the circle (S1) into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered...

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied...

hodological space while the former by ambient space. An ambient space or ambient configuration space is the space surrounding an object. According to this...

or surface is contained in a larger space, curvature can be defined extrinsically relative to the ambient space. Curvature of Riemannian manifolds of...

land', and μέτρον (métron) 'a measure') is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position...

In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from Ancient Greek: ὁμός homós...

In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric...

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n {\displaystyle n} -dimensional...

their representations in vector spaces and through matrices. Linear algebra is central to almost all areas of mathematics. For instance, linear algebra...

in mathematical morphology Scaling (geometry), including: Homogeneous dilation (homothety), the scalar multiplication operator on a vector space or affine...

In mathematics, the tangent space of a manifold is a generalization of tangent lines to curves in two-dimensional space and tangent planes to surfaces...

tangent space to M {\displaystyle M} . On the other hand the normal curvature depends strongly on how the submanifold lies in the ambient space, but marginally...

reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space. Topological surfaces...

In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature...

In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is...

mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, E 3 {\displaystyle \mathbb {E} ^{3}} . Two mathematical knots...

Subsurface mapping by ambient noise tomography can be applied in different fields, such as detecting the underground void space, monitoring landslides...

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E}...

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors...

topological spaces, such as Grothendieck topology, have provided applications to mathematical logic and to number theory. In many mathematical branches,...

It also serves as a counterexample to the claim that all Cantor spaces are ambiently homeomorphic to each other. It was discovered by Louis Antoine (1921)...