3. Let B be the collection of all open intervals (a, b) in R with a <b and a and brational numbers. Prove that B is a basis for the euclidean topology on R. 4. A topological space (X,T) is said to satisfy the second axiom of countability or to be second countable if there exists a basis B for T, where B consists of only a countable number of sets. (i) Using Exercise 3 above show that R satisfies the second axiom of countability.