F is closed.
F is compact. Prove that E\F is not necessarily compact
Mathematics Homework Solutions
#60710
Prove: Set Theory, closed sets and compact sets
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)
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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
This solution is comprised of a detailed explanation to prove that E R is closed.
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