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Prove that $[0,1]$ is not a compact subset of $\mathbb{R}$ with the lower limit topology, i.e. open sets are of the form $[a,b)$. - Mathematics Stack Exchange
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Prove that $[0,1]$ is not a compact subset of $\mathbb{R}$ with the lower limit topology, i.e. open sets are of the form $[a,b)$. - Mathematics Stack Exchange
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![SOLVED: We know that the set S = 1/n: n ∈ N is not compact because 0 is a limit point of S that is not in S. To see the non-compactness SOLVED: We know that the set S = 1/n: n ∈ N is not compact because 0 is a limit point of S that is not in S. To see the non-compactness](https://cdn.numerade.com/ask_previews/0d87dd7a-7225-4149-9314-f7c9e07d04da_large.jpg)
SOLVED: We know that the set S = 1/n: n ∈ N is not compact because 0 is a limit point of S that is not in S. To see the non-compactness
![Prove that $[0,1]$ is not a compact subset of $\mathbb{R}$ with the lower limit topology, i.e. open sets are of the form $[a,b)$. - Mathematics Stack Exchange Prove that $[0,1]$ is not a compact subset of $\mathbb{R}$ with the lower limit topology, i.e. open sets are of the form $[a,b)$. - Mathematics Stack Exchange](https://i.stack.imgur.com/6JDFA.png)