MAA 4211 Assigment 4
Due date: Wed. 10/17/01

• A: Without reading Rosenlicht's proof, prove parts (3) and (4) of the second proposition on p. 41. If you get stumped, read Rosenlicht's proof.

• B: In the metric space E¹ find an example illustrating that an infinite union of closed subsets need not be closed. (Note: Eⁿ means Rⁿ with the Euclidean metric.) Justify your answer (i.e. prove the non-closedness of the set you're claiming isn't closed). Hand this in.

• C: pp. 61-63/ 8,12,14. [#24, originally listed here, has been moved to the next assignment.] (Note: in #8 you are going to have to correctly define what it means for the points in an infinite sequence to be ``reordered''. See me if you have trouble defining this.) Hand all these in.

• D: Read the exam-solution handout. (This will be a physical handout, not a web handout; it should exist by Friday 10/12/01.)