(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If [tex]E_{1}[/tex],.....[tex]E_{n}[/tex] are compact, prove that E=[tex]\cup^{n}_{i=1}[/tex][tex]E_{i}[/tex] is compact.

2. Relevant equations

3. The attempt at a solution

A set E is compact iff for every family {[tex]G_{\alpha}[/tex]}[tex]_{\alpha\in}A[/tex] of open sets such that E[tex]\subsetU_{\alpha\in}A G_{\alpha}[/tex]

Let [tex]G_{\alpha}[/tex]=[tex]E_{n}[/tex].

Let E=(i,n)

If i<x<n, there is a positive integer n such that [tex]E_{n}[/tex]<x, hence x[tex]\in[/tex][tex]G_{n}[/tex] and E[tex]\subset[/tex][tex]G_{n}[/tex].

Not quite sure about this one.

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# Homework Help: Proving compactness

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