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LM, N, and A be C manifolds and pi: M x N M, p2: M x N → N be projections to the factors. For (a, b) e M x N, let i: M M x N be defined by i (p) = (p. b) and j: N P1. p2, i, and j are C mappings. Show that a mapping F: A → M x N is C* if and only if fi = pio F and f2 = p2 o F are C: - M x N by j(q) = (a, q). Show that %3D %3D ->

LM, N, and A be C manifolds and pi: M x N M, p2: M x N → N be projections to the factors. For (a, b) e M x N, let i: M M x N be defined by i (p) = (p. b) and j: N P1. p2, i, and j are C mappings. Show that a mapping F: A → M x N is C* if and only if fi = pio F and f2 = p2 o F are C: - M x N by j(q) = (a, q). Show that %3D %3D ->

Elements Of Modern Algebra
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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Lt M, N, and A be C manifolds and p1: M x N M, p2: M x N N be projections to the factors. For (a, b) eM x N, let i: M M x N be defined by i (p) = (p, b) and j: N M x N by j(g) = (a, q). Show that P1. p2, i, and j are C mappings. Show that a mapping F: A M x N is C if and only if fi = pi o F and f2 p2 o F are C. -> %3D %3D
Transcribed Image Text:Lt M, N, and A be C manifolds and p1: M x N M, p2: M x N N be projections to the factors. For (a, b) eM x N, let i: M M x N be defined by i (p) = (p, b) and j: N M x N by j(g) = (a, q). Show that P1. p2, i, and j are C mappings. Show that a mapping F: A M x N is C if and only if fi = pi o F and f2 p2 o F are C. -> %3D %3D
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