Question

show that every non-empty open set is a union of open intervals​

Answer 1

Answer:

Every open set in R is the union of disjoint open intervals. ... Figure that any member of a nonempty open subset A of R is part of some open interval within A. By properties of intervals in R, that interval contains a rational. With this reasoning, then, we can get an open interval corresponding to any point in A.

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Answer 2

Answer:

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