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I'm having trouble finding an open cover as described above. This question has been asked before here: find a open cover for R that has no lebesgue number.

However, I believe the only answer presented is wrong as the open cover suggested does not contain 0. If I'm mistaken, please let me know and I will use their answer. Otherwise, this question deserves to be revisited.

Community
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gbnhgbnhg
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    It's a careless error. Just define $$ B_n := (n-\frac 1{|n|+1}, n+\frac1{|n|+1}) $$ instead so that we can include a $B_0$. – Ben Grossmann Nov 28 '16 at 15:54

1 Answers1

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The solution in the other thread can be salvaged. The problem is that $B_0$ is ill-defined, since it includes a division by zero (also, there is a problem with negative $n$). Changing the definition to

$$B_n = \left(n - \frac{1}{|n| + 1}, n + \frac{1}{|n| + 1}\right)$$ yields an example by the same argumentation.

Dominik
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