How do you solve the second question? Let A, B C R. We define the distance between A and B byd(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 wheno A and Bare merely closed;o A and Bare open and bounded.

For second one we can take any two open interval one of whose right end point ar same of the others…

Answered: A and Bare open and bounded.

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A and Bare open and bounded.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.4: Cicumference And Area Of A Cicle

Problem 21E: Let N be any point on side BC of the right triangle ABC. Find the upper and lower limits for the...

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Question

How do you solve the second question?

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.

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