Consider the following collections of subsets of R:
B1 ={(a,∞):a∈R},
B2 ={(−∞,a):a∈R},
B3 ={[a,∞):a∈R},
B4 = {[a, b] : a, b ∈ R},
B5 = {[a, b] : a, b ∈ Q},
B6 ={[a,b]:a∈R,b∈Q}.
(i) Show that each of these is a basis for a topology on R.
(ii) What can you say about the corresponding topologies
T1,...,T6, eg, are any of the topologies the same, are any
comparable, are any equal to familiar topologies on R, etc?