5. We will say that a set S C R is an open set if for every x E S, there exist real numbers a and b such that a < x < b

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5 We Will Say That A Set S C R Is An Open Set If For Every X E S There Exist Real Numbers A And B Such That A X B 1 (70 KiB) Viewed 21 times

5. We will say that a set S C R is an open set if for every x E S, there exist real numbers a and b such that a < x < b and (a, b) CS. In short, every point in S lies on an open interval entirely contained within S. Recall that a set T is a closed set if and only if its complement T is an open set. Also, recall that any union of open sets is an open set. a. Show that any interval of the form (-0, a) is an open set. b. Show that any interval of the form (b, 0) is an open set. C. Show that any closed interval [a, b] is a closed set.