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

# Lie Group Quotient 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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## Cite this as:

Rowland, Todd. "Lie Group Quotient Space." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/LieGroupQuotientSpace.html