quotient space
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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”, in 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).
Synonyms
[edit]- (space composed of points equivalent to each other in some relation): identification space
Related terms
[edit]Translations
[edit]a topological space
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See also
[edit]- equivalence class
- quotient group (group theory)
Further reading
[edit]- Quotient space on Wikipedia.Wikipedia
- Equivalence class on Wikipedia.Wikipedia