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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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