For two non-empty sets of numbers A and B, define A +B to be the set of all sums a + b where a is in A and b is in B. Show that if A is open, then A +B is open. Show that if A and B are compact, then A+ B is compact. Give an example where A and B are closed but A+ B is not.
For two non-empty sets of numbers A and B, define A +B to be the set of all sums a + b where a is in A and b is in B. Show that if A is open, then A +B is open. Show that if A and B are compact, then A+ B is compact. Give an example where A and B are closed but A+ B is not.
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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