Thus if 𝔇 is an arbitrary decomposition of a space X into mutually disjoint subsets, then the corresponding quotient space is obtained by 'shrinking' or 'identifying' each member of 𝔇 to a single point. For this reason, the quotient spaces are sometimes called identification spaces and quotient maps as identification maps.

1989, unnamed translator, Nicolas Bourbaki, Elements of Mathematics: General Topology: Chapters 1-4, [1971, N. Bourbaki, Éléments de Mathématique: Topologie Générale 1-4, Masson], Springer, page 110,
PROPOSITION 6. Every quotient space of a connected space is connected.

The quotient space obtained from such a relation is called extended Reeb (ER) quotient space. Moreover, the ER quotient space, which is an abstract sub-space of M* and is independent from the geometry, may be represented as a traditional graph, which is called the extended Reeb graph (ERG).

Quotient space

Meaning

Noun

Synonyms