Separable and normal topologies

  • #1
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.

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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