6. Suppose M and N are C manifolds, U an open set of M, and F: U Nis C. Show that there exists a neighborhood V of any p eU, V CU, suchthat F can be extended to a C mapping F*: M N with F(q) = F*(q)for all q e V.

Answered: Image /qna-images/answer/26bb63f5-2806-480b-bd3f-fe3f823185ff.jpg

Answered: 6. Suppose M and N are C manifolds, U…

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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If x and y are elements of an ordered integral domain D, prove the following inequalities. a. x22xy+y20 b. x2+y2xy c. x2+y2xy
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27. Let , where and are nonempty. Prove that has the property that for every subset of if and only if is one-to-one. (Compare with Exercise 15 b.). 15. b. For the mapping , show that if , then .
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The main point of this exercise is to use Green’s Theorem to deduce a specialcase of the change of variable formula. Let U, V ⊆ R2 be path connected open sets and letG : U → V be one-to-one and C2such that the derivate DG(u) is invertible for all u ∈ U.Let T ⊆ U be a regular region with piecewise smooth boundary, and let S = G(T). Answer C
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6. Suppose M and N are C manifolds, U an open set of M, and F: U N is C. Show that there exists a neighborhood V of any p e U, VCU, such that F can be extended to a C mapping F*: M N with F(q) = F*(q) for all q e V.

6. Suppose M and N are C manifolds, U an open set of M, and F: U N is C. Show that there exists a neighborhood V of any p e U, VCU, such that F can be extended to a C mapping F: M N with F(q) = F(q) for all q e V.