Real coordinate space
（重定向自Usual topology）
![The Cartesian product structure of R2 on Cartesian plane of ordered pairs (x, y). Blue lines denote coordinate axes, horizontal green lines are integer y, vertical cyan lines are integer x, brown-orange lines show half-integer x or y, magenta and its tint show multiples of one tenth (best seen under magnification)](/Images/godic/202502/19/Real_2-space_as_square_grid4938.png")
![The n-simplex (see below) is the standard convex set, that maps to every polytope, and is the intersection of the standard (n + 1) affine hyperplane (standard affine space) and the standard (n + 1) orthant (standard cone).](/Images/godic/202502/19/2D-simplex.svg4938.png")
![Both hypercube and cross-polytope in R2 are squares, but coordinates of vertices are arranged differently](/Images/godic/202502/19/Real_2-space,_orthoplex.svg4938.png")
![Cube (the hypercube) and octahedron (the cross-polytope) of R3. Coordinates are not shown](/Images/godic/202502/19/Duality_Hexa-Okta_SVG.svg4938.png")
In mathematics, real coordinate space of n dimensions, written R (/ɑːrˈɛn/ ar-EN) (R with superscript n, also written ℝ with blackboard bold R) or R^n with keyboard is a coordinate space that allows several (n) real variables to be treated as a single variable. With various numbers of dimensions (sometimes unspecified), R is used in many areas of pure and applied mathematics, as well as in physics. It is the prototypical real vector space and a frequently used representation of Euclidean n-space. Due to the latter fact, geometric metaphors are widely used for R, namely a plane for R and three-dimensional space for R.