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A Set Theory and Metric Spaces book asks Dick CheneyQ: Let f and g be commuting maps on a complete metric space. Suppose that f is a strict contraction (g need not be continuous). Prove that there exists a unique joint fixed point for f and g.A: We're all a little weary of the Clinton-Gore routine. Q: Let M be a metric space. Prove that M is separable if and only if every collection of disjoint open sets of M is countable. A: In the end, George W. Bush will defeat this vice president, and I will replace him [sic]. Q: Let X and Y be any metric spaces. Prove that the natural projection of X >< Y onto X is open (i.e., it sends open sets into open sets). A: Politics has become a war by other means, an endless onslaught of accusation, a constant setting of groups one against the other...This is what Bill Bradley was up against, and others before him. Q: Call a subset B of a set A cofinite if the complement of B in A is finite. If B and C are cofinite subsets of A, prove that B intersect C is cofinite. A: He will show us that national leaders can be true to their word...and that they can get things done by reaching across the partisan aisle, and working with political opponents in good faith and common purpose. Q: Let C be a chain which every subset has a top element or a bottom element (or both). Prove that C consists of a well-ordered set surmounted by the dual of a well-ordered set. A: Does anyone, Republican or Democrat [there can be not others. -ed], seriously believe that under Mr. Gore, the next four years would be any different from the last eight? They came in together, now let us see them off together.
(Questions from Set Theory and Metric Spaces, by Kaplansky, I.,
Answers by Dick Cheney as reported by CNN.com)
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