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31. Suppose f: [a, b] → R and g: [a, b] → R are both continuous. Let T = {x: f(x) = g(x)} Prove that T is closed.

31. Suppose f: [a, b] → R and g: [a, b] → R are both continuous. Let T = {x: f(x) = g(x)} Prove that T is closed.

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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You may use basic facts about sequences without proof.

31. Suppose f: [a, b] → R and g: [a, b] → R are both continuous. Let T = {x: f(x) = g(x)} Prove that T is closed.
Transcribed Image Text:31. Suppose f: [a, b] → R and g: [a, b] → R are both continuous. Let T = {x: f(x) = g(x)} Prove that T is closed.
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