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Suppose q: X →Y is a quotient map and that it is one-to-one. Show that q is a homeomorphism. (Hint: Since q is injective, for any A C X,q¬'(q(A)) = A)).

Suppose q: X →Y is a quotient map and that it is one-to-one. Show that q is a homeomorphism. (Hint: Since q is injective, for any A C X,q¬'(q(A)) = A)).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.2: Ring Homomorphisms
Problem 11E: 11. Show that defined by is not a homomorphism.
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Suppose q: X →Y is a quotient map and that it is one-to-one. Show that q is a homeomorphism. (Hint: Since q is injective, for any A C X,q¬(q(A)) = A)).
Transcribed Image Text:Suppose q: X →Y is a quotient map and that it is one-to-one. Show that q is a homeomorphism. (Hint: Since q is injective, for any A C X,q¬(q(A)) = A)).
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