Let ECR be defined by E = { n E N}. Prove the following by appealing...

 

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Let ECR be defined by E = { n E N}. Prove the following by appealing only to the definition of compactness, without using the Heine-Borel theorem. (a) Prove that E is not compact. In other words, find an open cover of E with no finite subcover. Let ECR be defined by E = { n E N}. Prove the following by appealing only to the definition of compactness, without using the Heine-Borel theorem. (a) Prove that E is not compact. In other words, find an open cover of E with no finite subcover.

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Let SS and TT both be compact sets in RnRn Show that STST is also compact using the open cover d... View the full answer