Explore Subspace on MathWorld

A subspace is a subset of a vector space that is also itself a vector space. This term can also be used for a subset of a topological space.

Subspace is a college-level concept that would be first encountered in a topology course covering point-set topology.


Topological Space: A topological space is a set with a collection of subsets T that together satisfy a certain set of axioms defining the topology of that set.
Vector Space: A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space.

Classroom Articles on Point-Set Topology

  • Closed Set
  • Open Set
  • Homeomorphism
  • Point-Set Topology
  • Neighborhood

  • Classroom Articles on Topology (Up to College Level)

  • Dimension
  • Projective Plane
  • Metric
  • Projective Space
  • Metric Space
  • Topology
  • Möbius Strip
  • Torus