A Lie group quotient space 
is the set
of left cosets of a subgroup 
of a Lie group 
, equipped with the quotient topology
from 
.
More generally, this construction applies to a topological
group 
.
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, TransitivePortions of this entry contributed by Todd Rowland
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Cite this as:
Weisstein, Eric W., with contributions by Todd Rowland. "Lie Group Quotient Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/LieGroupQuotientSpace.html