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Transcript

Homework M472 Fall 2014 Exercise 1. Prove that R2 \ (0, 0) (the plane minus the origin) with euclidean topology is connected. Exercise 2. Is R with the finite complement topology connected? Exercise 3. Assuming that you know that R (with euclidean topology) is connected, prove that the circle (with euclidean topology) is also connected. Can you somehow ”adapt” this argument to prove that the circle with the finite complement topology is connected? Exercise 4. Let (X, τX ) be a connected topological space and (Y, τdisc ) be a topological space with the discrete topology. What are the continuous functions from X to Y ?