A symmetric space is, in differential geometry and representation theory, a smooth manifold whose group of symmetries contains an "inversion symmetry" about every point. Examples include:
- Riemannian symmetric space
- Hermitian symmetric space
- Quaternion-Kähler symmetric space
- Weakly symmetric space
In topology, symmetric space may also refer to:
- R0 space, a topological space in which two topologically distinguishable points can be separated
In computational complexity theory, symmetric space may refer to undirected or reversible analogues of nondeterministic space complexity, for instance:
- SL (complexity), the class of problems solvable in logarithmic symmetric space
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