Open Set Proof Let O be a bounded open set in R^n and let K be a compact set in
ID: 2980474 • Letter: O
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Open Set Proof Let O be a bounded open set in R^n and let K be a compact set in R^n. Denote Br(u) as a ball around some point u in R^n *Show by construction that there does not exist an r > 0 with Br(u) contained in O for every u in O. Since we know that O is open, we also know that by limits that you can always find a smaller r as you approached the boundary of O. Second part of the Question: What would happen if O were unbounded? Close Set Proof Now suppose that there's a K contained in O and let K be compacted. *Prove that there is some positive r > 0 such that Br(u) contained in O for every u in K. *Requires concise proof and construction.Explanation / Answer
Suppose that E c had a limit point x that was not in E c ; then x would belong to E and therefore would not in fact be a limit point of E c . In other words, if nothing in E is a limit point of E c , then any limit points that E c might have can
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