quotient space
See also: quotient-space
English[edit]
Noun[edit]
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 is an arbitrary decomposition of a space into mutually disjoint subsets, then the corresponding quotient space is obtained by 'shrinking' or 'identifying' each member of to a single point. For this reason, the quotient spaces are sometimes called identification spaces and quotient maps as^{[sic]} 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.
- 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) 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).
- 1983, K. D. Joshi, Introduction to General Topology, New Age International, page 129,
Synonyms[edit]
- (space composed of points equivalent to each other in some relation): identification space
Related terms[edit]
See also[edit]
- equivalence class
- quotient group (group theory)
Further reading[edit]
- Equivalence class on Wikipedia.Wikipedia
- Quotient space (topology) on Wikipedia.Wikipedia