Explore Dimension on MathWorld

Dimension is a topological measure of the size of an object's covering properties, roughly corresponding to the number of coordinates needed to specify a point on the object.

Dimension is a college-level concept that would be first encountered in a topology course.


Euclidean Space: Euclidean space of dimension n is the space of all n-tuples of real numbers which generalizes the two-dimensional plane and three-dimensional space.
Line: A line is the infinite extension in both directions of a line segment, giving the path of shortest distance between two points in Euclidean space.
Plane: A plane is a two-dimensional surface defined by linear equations.
Point: A point is a zero-dimensional mathematical object that can be specified in n-dimensional space using n coordinates.

Classroom Articles on Topology (Up to College Level)

  • Closed Set
  • Point-Set Topology
  • Homeomorphism
  • Projective Plane
  • Metric
  • Projective Space
  • Metric Space
  • Subspace
  • Möbius Strip
  • Topological Space
  • Neighborhood
  • Topology
  • Open Set
  • Torus