(ii) Show that an open interval \((a,b)\) is an open set.
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Let x be any point in (a,b). Since x is in (a,b), we know that a < x < b. Let r be any positive number such that 0 < r < min(x-a, b-x). This ensures that the open ball B(x,r) centered at x with radius r is completely contained in (a,b). To see why this is true, Show more…
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