I would like to know how to construct a proof of union/and of 2 closed sets and how to prove compact sets.
(See attached file for full problem description)
a. Let E and F be closed sets in R. Prove that E R is closed. Prove the E F is closed.
b. Let E and F be compact sets in R. Prove that E F is compact. Prove that EF is not necessarily compact© BrainMass Inc. brainmass.com October 9, 2019, 5:33 pm ad1c9bdddf
Please see the attachment.
We know a set is closed if and only if , where is the set of all cluster points of .
(a) and are closed sets in .
First, I show that is closed in . For any , we can find a sequence , such that . Since each , then or . We can select the two subsequence ...
This solution is comprised of a detailed explanation to prove that E R is closed.