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