4. Suppose that V is a bounded, open set in Rn, and : V -+ Rn...
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4. Suppose that V is a bounded, open set in Rn, and ¢ : V -+ Rn is 1-1 and continuously differentiable on V with ~~ =f. 0 on V. Let W = {Wj }jEN be an open covering of V and {¢j }jEN be a CP partition of unity on V subordinate to W, where p ~ 1. Prove that {¢j 0 ¢-l }jEN is a C1 partition of unity on ¢(V)
subordinate to the open covering {¢(Wj)}jEN.
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