Dictionary

quotient space en · NOUN

Meanings

1. A space obtained from another by identification of points that are equivalent to one another in some equivalence relation.
   • Thus if #92;mathfrak#123;D#125; 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 #92;mathfrak#123;D#125; to a single point. For this reason, the quotient spaces are sometimes called identification spaces and quotient maps as^([sic]) identification maps. 1983, K. D. Joshi, Introduction to General Topology, New Age International, page 129:
   • 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). 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:
   • 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.

Forms

Relateds

quotient map · quotient topology · equivalence class · quotient group

Synonyms

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

Translations (1)

fi tekijäavaruus (a topological space)