4. A new topology on R If n 6 2+, dene a new basis En for a topology on R by adjoining to the usual basis of open sets the one-point set {R}. (a) Show that 13'n is indeed a basis for a topology. Let 7;, be the topology generated by B\". (b) Show that (R71) (that is, R with a topology for which {1} is open) and (R75) (here {2} is open) are homeomorphic but that '7] 7E 75. (c) Show that (R, 71) is not homeomorphic to R in the standard topology by describing a topological property that they don't have in common. Please be sure to Show that property you describe is topological (that is, that it is preserved under homeomorphism)