consider X=(-1,0) union (0,1) with the metric induced from R . Then {(-1,0),(0,1)} is an open cover for X. show that this cover has no Lebesgue number
Question
Solution 1
The Lebesgue number of an open cover of a metric space is a positive number such that every subset of the space with diameter less than this number is contained in some member of the cover.
In this case, we have the open cover {(-1,0),(0,1)} of the set X=(-1,0) union (0,1).
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