Phrase guide

quotient map

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

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.

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences, topology

Examples

  • 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 quotient topology) is topologically equivalent to a torus.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

No etymology was provided for this word.