we have defined open sets in R: for any a ∈ R, there is sigma >...

we have defined open sets in R: for any a ∈ R, there is sigma > 0 such that (a − sigma, a + sigma) ⊆ A.

(i) Let A and B be two open sets in R. Show that A ∩ B is open.

(ii) Let {Aα}α∈I be a family of open sets in R. Show that ∪(α∈I)Aα is open. Hint: Follow the definition of open sets.

Please be specific and rigorous! Thanks!

Expert Solution

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Colby Messinger answered 1 year ago

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