Three topological spaces are given below. Determine which ones are separable and which ones are normal.(Hint on the separability part: For one of the spaces it is easy to construct a countably dense set, for another space you can prove every infinitelycountable set is dense, and in the other space you can prove that every countabe set can not be dense.(adsbygoogle = window.adsbygoogle || []).push({});

a) X=R with the cofinite topology t1 = {U proper subset of R: R~ is finite is finite}

b) X=R with e co-countable topology, t2= {U proper subset of R: R~U is countable

c) X=R^2 with the Euclidean topology.

help...I have been working on topology problems all day

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# Separable and normal topologies

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