Exercise 4. Consider the following topologies on R: T = the standard topology T = the finite complement topology T3 = the lower limit topology, having all sets [a, b) as basis T = the upper limit topology, having all sets (a, b] as basis the topology having all sets (-, a) as basis T5 = Determine which are these topologies are finer / coarser than which of the others. Definition of the finite complement topology: the open sets are all sets whose complement in X is finite (and the empty set).