MATH 355 Final: MATH 355 Amherst S09M28Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 355
• Professor: All

Document Summary

Instructions: this exam is to be turned in no later than friday may 8th in class. You may use your book, your notes from class, and your problem sets, but no additional resources or discussion are permitted. If you need clari cation on a problem, please ask me. Each problem will be graded out of 8 points for a total of 64 possible points. Let a be the set of limit points of subsequences of (an). In other words, a a if and only if there exists a subsequence (ank ) such that (ank ) a. Determine the cardinality of the set {(x, y) | x, y q, x2 + y2 = 1}. (hint: consider lines through (0, 1). ) Let a, b r be nonempty disjoint compact sets. Show that a b is not connected. Let (x, d) be a metric space and let fn : x x be uniformly continuous for all n n.