Euclidean Space (redirected from Euclidean topology)

Euclidean space

In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between two points is given by a distance formula. The only conception of physical space for over 2,000 years, it remains the most compelling and useful way of modeling the world as it is experienced. Though non-Euclidean spaces, such as those that emerge from elliptic geometry and hyperbolic geometry, have led scientists to a better understanding of the universe and of mathematics itself, Euclidean space remains the point of departure for their study.

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euclidean space [yü′klid·ē·ən ′spās]

(mathematics)

A space consisting of all ordered sets (x₁, …,x_n) ofnnumbers with the distance between (x₁, …,x_n) and (y₁, …,y_n) being given bythe numbernis called the dimension of the space.

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Euclidean Space 

in mathematics, a space whose properties are described by the axioms of Euclidean geometry. In a more general sense, a Euclidean space is an n-dimensional vector space, into which several special Cartesian coordinates can be introduced so that its metric is defined in the following manner: If point M has the coordinates (x₁x₂, …, x_n and point M^* has the coordinates (x₁^*, x₂^*, …, x_n^*), then the distance between these points is