A and Bare open and bounded.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
How do you solve the second question?
Transcribed Image Text:Let A, B C R. We define the distance between A and B by
d(A, B) = inf{|x - y| : x E A, y E B}.
Show that if A is compact and B is closed, and d(A, B) = 0, then ANB#Ø.
• Give examples of d(A, B) = 0, ANB=Ø when
o A and Bare merely closed;
o A and Bare open and bounded.
Expert Solution
Step 1
For second one we can take any two open interval one of whose right end point ar same of the others left end point.
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