MATH 4565 Study Guide - Midterm Guide: Homeomorphism, Continuous Function, Identity Function
9 Jan 2019
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Why, or why not: let p : x y be a continuous map. Suppose there is a continuous map f : y x such that p f equals the identity map of y . Show that p is a quotient map: let f : x y and g : x y be two continuous maps. Suppose y is a hausdor space, and that there is a dense subset d x such that f (x) = g(x) for all x d. Show that f (x) = g(x) for all x x: let x = {1, 2, 3, 4}, equipped with the topology. T = { , {1}, {2}, {1, 2}, {3, 4}, {2, 3, 4}, {1, 3, 4}, {1, 2, 3, 4}}. If not, explain why not: suppose x is homeomorphic to x and y is homeomorphic to y .
