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, TransitiveThis 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. https://mathworld.wolfram.com/LieGroupQuotientSpace.html