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tylerc1991
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Homework Statement
Give an example of a topological space (X,T) that is separable and Hausdorff, with a subspace (A,T_A) that is not separable.
The Attempt at a Solution
Let X = R and T be a topology on X whose basis elements are open intervals intersected with the rationals and individual irrational numbers, essentially the discrete topology on the irrationals. Then T is Hausdorff and separable, and has a subspace (the irrationals) that is not separable.