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4. Let f: RR. For each subset ACR, we define its preimage by f¹(A) = { € R" | f(x) = A}. we assume that f is continuous. Prove that for every compact KCR", f(K) is compact in R.

4. Let f: RR. For each subset ACR, we define its preimage by f¹(A) = { € R" | f(x) = A}. we assume that f is continuous. Prove that for every compact KCR", f(K) is compact in R.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...
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4. Let f: RR. For each subset ACR, we define its preimage by f¹(A) = { € R" | f(x) = A}. we assume that f is continuous. Prove that for every compact KCR", f(K) is compact in R.
Transcribed Image Text:4. Let f: RR. For each subset ACR, we define its preimage by f¹(A) = { € R" | f(x) = A}. we assume that f is continuous. Prove that for every compact KCR", f(K) is compact in R.
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