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kathrynag
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Homework Statement
Let E be compact and nonempty. Prove that E is bounded and that sup E and inf E both belong to E.
Homework Equations
The Attempt at a Solution
E is compact, so for every family{[tex]G_{\alpha}[/tex]}[tex]_{\alpha\in}A[/tex] of open sets such that E[tex]\subset[/tex][tex]\cup_{\alpha\in}A[/tex][tex]G_{\alpha}[/tex], there is a finite set{a1,a2...,an}[tex]\subset[/tex]A such that E[tex]\subset[/tex][tex]\cup^{n}_{i=1}[/tex][tex]G_{\alpha_{i}}[/tex]