If $A, B$ are two open sets in $\mathbb R$ such that $A\cap B$ is compact, then show that $A\cap B =\varnothing$.
Since A is open then int$(A)\subseteq A$, and same thing for $B$, but I can't solve this.
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What is $\phi$ in this context? – mathisfun May 05 '17 at 16:29
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@mathisfun probably $\emptyset$ – supinf May 05 '17 at 16:29
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@supinf Thanks, it makes sense now. I edited to reflect this. – mathisfun May 05 '17 at 16:32
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hint:
Keep in mind that the intersection of open sets is open again. Do you know any set that is both open and compact?
supinf
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