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Prove that if E ⊂ R is bounded and sup E ∈ E or inf E...

Prove that if E ⊂ R is bounded and sup E ∈ E or inf E ∈ E, then E is not open.

Analysis question (R refers to the real numbers).

Math   Advanced-Math   
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Answer #1

I have used the definition of open sets in Real number .A set E is called an open set in R if for every x in E ,there exist an r>0 such that (x-r,x+r) is subset of E.I hope you like this.

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