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

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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.
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern