Noun
quotient space (plural quotient spaces)
(topology and algebra) A space obtained from another by identification of points that are equivalent to one another in some equivalence relation.
A normal subgroup of a topological group, acting on the group by translation action, is a quotient space in the senses of topology, abstract algebra, and group actions simultaneously. Source: Internet
For a properly discontinuous action, cocompactness is equivalent to compactness of the quotient space X/G. Source: Internet
A topological group G is Hausdorff if and only if the trivial one-element subgroup is closed in G. If G is not Hausdorff then one can obtain a Hausdorff group by passing to the quotient space G/K where K is the closure of the identity. Source: Internet
For finite dimensions, this means that the dimension of the quotient space W/f(V) is the dimension of the target space minus the dimension of the image. Source: Internet
Given a subspace M ⊂ X, the quotient space X/M with the usual quotient topology is a Hausdorff topological vector space if and only if M is closed. Source: Internet
Gluing edges of polygons is a special kind of quotient space process. Source: Internet