MATH 320 Midterm: MATH 320 2012 Winter Test 1
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You can use parts of problems to prove other parts without having done the parts you use. Page 2 of 10: de ne (a) (3 points) lim inf an (b) (4 points) limx a f (x) (c) (3 points) metric. Page 3 of 10: let x, y be sets and let f : x y . Let a be any subset of x and let b any subset of. Y . (a) (2 points) de ne f 1(b). (b) (2 points) de ne f (a). (c) (6 points) which of the following statements is true for all x, y, a, f ? (i) f 1(cid:0)f (a)(cid:1) = A; (ii) f 1(cid:0)f (a)(cid:1) a; (iii) f 1(cid:0)f (a)(cid:1) a. Page 4 of 10: [0, 1] is an interval of the real line. For an integer n 0 let dn be the subset of [0, 1] , an are each either 0 or 1. consisting of all points d = a0.
