Lie Group Quotient Space

The set of left cosets of a subgroup H of a topological group G forms a topological space. Its topology is defined by the quotient topology from pi:G->G/H. Namely, the open sets in G/H are the images of the open sets in G. Moreover, if H is closed, then G/H is a T2-space.

See also

Effective Action, Free Action, Group, Group Orbit, Group Representation, Isotropy Group, Matrix Group, Quotient Space, Topological Group, Transitive

This entry contributed by Todd Rowland

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Rowland, Todd. "Lie Group Quotient Space." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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