quotient space

Noun

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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.**1983**, K. D. Joshi,*Introduction to General Topology*, New Age International, page 129 ↗,- Thus if \mathfrak{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 \mathfrak{D} to a single point. For this reason, the**quotient spaces**are sometimes called**identification spaces**and**quotient maps**as^{[sic]}**identification maps**.

- Thus if \mathfrak{D} is an arbitrary decomposition of a space X into mutually disjoint subsets, then the corresponding
**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.

- PROPOSITION 6.
**2004**, Silvia Biasotti, Bianca Falcidieno, Michela Spagnuolo,*6: Surface Shape Understanding Based on Extended Reeb Graphs*, Sanjay Rana (editor),*Topological Data Structures for Surfaces: An Introduction to Geographical Information Science*, Wiley, page 96 ↗,- The
**quotient space**obtained from such a relation is called*extended Reeb*(*ER*). Moreover, the ER*quotient space***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*).

- The

- (
*space composed of points equivalent to each other in some relation*) identification space

- quotient map
- quotient topology

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