The idea is to prove that the open intervals (like $]a,b[$) are contained in the topology of the left-closed sets ($[a,b[$), but I cannot see a way of generating open sets from half-closed sets. (Same goes for the right-closed sets)
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2 Answers
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$ ]a,b[ = \bigcup_{n\in\mathbb{N}} [a + \frac{1}{n},b[$
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$\begingroup$ This does not provide an answer to the question. Once you have sufficient reputation you will be able to comment on any post; instead, provide answers that don't require clarification from the asker. - From Review $\endgroup$ Nov 1, 2022 at 22:53
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2$\begingroup$ @Leucippus This is exactly the answer I would expect. It doesn't require any clarification. $\endgroup$ Nov 1, 2022 at 23:15
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Hint: Note that the sequence $\frac1n\to 0$, but $0\notin\{\frac1n:n\in\mathbb N\}$.
Can you think of a way to use this with a family of intervals to prove what you want?
