Final Exam

Wednesday, December 16, 2015

14:42

Machine generated alternative text:
1. (30 pts) Let X — IR x IR with the order topology induced by the dictionary order. Let
Q denote the set of all rational numbers.
(a) Is Q x IR an open subset of X? Prove that your answer is correct.

Machine generated alternative text:
3. (30 pts) Let X Z+ the the finite complement topology, Y Z+ with the discrete
topology and W X x Y with the product topology.
(a) Is the set I (m, n) e W : m n) open in W? Prove that your answer is correct.

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