MATH 411 Study Guide - Open Set, Triangle Inequality, Rational Number
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Math 411 spring 2013 boyle exam 1: (5 points) suppose that a distance d on r2 is de ned from the norm. Draw a picture of the set {x r2 : d(x, 0) = 1}, where 0 denotes the origin: (15 points) state the cauchy schwarz inequality. Then use it to prove the triangle inequality: (16 points) suppose f is a function from a metric space x to a metric space y . No proof necessary. (c) suppose f : e rk is continuous and e is a closed bounded subset of. Give a short proof that f (e) is a closed bounded subset of rk. (appeal to general results, which you do not have to reprove. ) On the other side of this paper: (35 points) for each of the following, answer true or false. If {un : n = 1, 2, . is a collection of open sets, then their union a.
