sample midterm 1

# sample midterm 1 - THE UNIVERSITY OF MARYLAND COLLEGE PARK...

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THE UNIVERSITY OF MARYLAND COLLEGE PARK MD Daniel R. Vincent ECONOMICS 600 September 18, 2001 Office: 4128b Phone: 301 405 3485 Mathematical Economics: Mid Midterm Test No books or notes are allowed. If necessary to derive an answer you make additional assumptions, however, be explicit about what you are assuming and recall that answers invoking the fewest number of assumptions are better. 1.(40 points) Provide an example of the following or prove why such an example cannot exist: i) A set whose interior is connected but whose closure is not connected. Consider the set (0,1) c 2. The closure of this set is [0,1] c 2 which is not connected but the interior is (0,1) which is connected. ii) A set which does not contain any convex subsets. Either a set is empty or non-empty. The empty set is (trivially) convex. Any non-empty set contains a subset of a single element which is again (almost trivially) convex. (The definition does not require that the two points that you are drawing a line between are different.) iii) Two sequences each of which converges but whose difference does not converge.

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