Let f: X→ Y be a map between the sets X and Y. (a) Show that f is injective if and only if there exists a map g: Y → X so that go f = idx. (b) Show that f is surjective if and only if there exists a map h: Y → X so that foh = idy.
Let f: X→ Y be a map between the sets X and Y. (a) Show that f is injective if and only if there exists a map g: Y → X so that go f = idx. (b) Show that f is surjective if and only if there exists a map h: Y → X so that foh = idy.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.2: Mappings
Problem 27E: 27. Let , where and are nonempty. Prove that has the property that for every subset of if and...
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Transcribed Image Text:Let f : X → Y be a map between the sets X and Y.
(a) Show that f is injective if and only if there exists a map g : Y → X so that
go f = idx.
(b) Show that f is surjective if and only if there exists a map h : Y → X so that
foh = idy.
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