Übersetzung für '
quotient set' von Englisch nach Deutsch
| NOUN | a quotient set | quotient sets |
NOUN article.ind sg | pl
21 Übersetzungen
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Anwendungsbeispiele Englisch
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- In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes).
- This distinction gives rise to the notion of a quotient set.
- Often in mathematics, when one defines an equivalence relation on a set, one immediately forms the quotient set (turning equivalence into equality).
- However, if sets whose symmetric difference has measure zero are identified into a single equivalence class, the resulting quotient set can be properly metrized by the induced metric.
- Thus, we have a quotient set S/~ of equivalence classes of S, which forms a partition of S.
- Note that the specific quotient set depends on a choice of maximal torus, but the resulting groups are all isomorphic (by an inner automorphism of "G"), since maximal tori are conjugate.
- is the quotient set of "X" by ~. If "X" is a topological space, there is a natural way of transforming [...] into a topological space; see quotient space for the details.
- If [...] is a discrete group then a lattice in [...] is exactly a subgroup [...] of finite index (i.e. the quotient set [...] is finite).
- In other words: the atoms are a partition of [...]; [...] is the corresponding quotient set; and [...] is the corresponding canonical surjection.
- This quotient set [...] is called the "coimage" of the function [...] and denoted [...] (or a variation).
© dict.cc English-German dictionary 2024
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