In
topology and related areas of
mathematics, a
quotient space (also called an
identification space) is, intuitively speaking, the result of identifying or "gluing together" certain points of a given
topological space. The points to be identified are specified by an
equivalence relation. This is commonly done in order to construct new spaces from given ones. The
quotient topology consists of all sets with an
open preimage under the
canonical projection map that maps each element to its equivalence class.