In mathematics, a space is a collection of any number of sets with added structure.

Mathematical spaces often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space. For instance, all inner product spaces are also normed vector spaces, because the inner product induces a norm on the inner product space such that:

$|x|\; =sqrt\{langle\; x,\; xrangle\}.$

See also

• Affine space
• Banach space
• Cauchy space
• Euclidean space
• Function space
• Hilbert space
• Inner product space
• Kolmogorov space
• Measure space
• Metric space
• Minkowski space
• Normed vector space
• Quotient space
• Topological space
• Uniform space
• Vector space