Math 127C Homework 2 1. (6 points) Show that a finite union of compact sets is compact. Give an example of an infinite union of compact sets which is not compact. 2. (6 points) Let f : [0, 1] ? R3 be a continuous function. Let R3 have the usual Euclidean coordinates (x, y, z), and suppose f (0) = (?10, 5, 7) and f (1) = (10, 3, 3). Show that Im(f ) intersects the plane in R3 given by x = 0. 3. (6 points) Munkres 1.4.1(a) 4. (7 points) Munkres 1.4.2
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