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(a) Prove that if A and B are open, then A+ B is open.

(a) Prove that if A and B are open, then A+ B is open.

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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For sets A and B, define A+ B = {a +b: a € A, b e B}. (a) Prove that if A and B are open, then A+ B is open. (b) Prove that if A and B are compact, then A+ B is compact. (c) It is not true that the sum of closed sets must be closed. Provide an example to demonstrate this.
Transcribed Image Text:For sets A and B, define A+ B = {a +b: a € A, b e B}. (a) Prove that if A and B are open, then A+ B is open. (b) Prove that if A and B are compact, then A+ B is compact. (c) It is not true that the sum of closed sets must be closed. Provide an example to demonstrate this.
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