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3. Let f A → X be a function such that A CX. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x € A} is bounded.

3. Let f A → X be a function such that A CX. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x € A} is bounded.

Advanced Engineering Mathematics
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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3. Let f A X be a function such that AC X. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x € A} is bounded.
Transcribed Image Text:3. Let f A X be a function such that AC X. Show that if A is compact, then the range of f defined by f(A) = {f(x) : x € A} is bounded.
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