# Subspace

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.

### Prerequisites

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. |