quotient map
quotient map noun: a surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space.
Noun
quotient map (plural quotient maps)
- A surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space.
- If the square #91;0,1#93;#92;times#91;0,1#93; (with the subspace topology) in #92;mathbb#123;R#125;² (with the standard topology) is mapped onto the set #91;0,1)#92;times#91;0,1) with the quotient map f(x,y)#61;(#92;lfloorx#92;rfloor,#92;lfloory#92;rfloor), then the target space (with its induced...
- Synonyms:
- identification map
Synonyms of quotient map
Forms of quotient map
| plural | quotient maps |
|---|
Questions about quotient map
- What does quotient map mean?
- Quotient map means a surjective, continuous function from one topological space to another one, such that the latter one's topology has the property that if the inverse image (under the said function) of some subset of it is open in the function's domain, then the subset is open in the target space.
- What part of speech is quotient map?
- Quotient map is a noun.
- What is the plural of quotient map?
- The plural of quotient map is quotient maps.
Words near quotient map in the dictionary
Source and license
Adapted from Wiktionary: quotient map (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “quotient map.” Word.ws, https://word.ws/quotient_map. Based on Wiktionary, CC BY-SA 4.0.