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tylerc1991
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Homework Statement
Give an example of a separable Hausdorff space (X,T) that has a subspace (A,T_A) that is not separable.
Homework Equations
A separable space is one that has a countable dense subset.
The Attempt at a Solution
Let (X,T) (i.e. the separable Hausdorff space) be the real number line with the usual topology. Now let the subspace (A,T_A) be the irrational numbers. The topology generated will in essence be the discrete topology. Since the irrational numbers are not countable they do not have a countable dense subset. If this is just rubbish can someone give me a kick in the right direction? Thank you very much!