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 isopen.
(ii) Let {A?}??I be a family of open sets in R. Show that?(??I)A? is open. Hint: Follow the definition of open sets.
Please be specific and rigorous! Thanks!
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