Symmetric space

In mathematics, the term symmetric space has several different meanings.

• In general topology, a symmetric space, or R₀ space, is a topological space whose Kolmogorov quotient is T₁. See R0 space.

• In differential geometry, including applications to general relativity, a symmetric space is a certain kind of homogeneous space in the theory of Lie groups. One characterisation is as G/H where G is a Lie group and H a subgroup that is the fixed set of a automorphism of G of order 2. There is a classification of such spaces, by Elie Cartan.

This is a disambiguation page.