Posted by J. Holmer on September 22, 2007, 4:08 pm, in reply to "HW4 #7" You are to show that the topological space (X,T) is separable iff (X,T) is second countable. You will in your proof have to use the fact that the topology T we are working with is defined by the metric \rho.
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Yes, the metric space (X, \rho) is given the topology generated by the balls defined by the \rho metric. Label this topology T.
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