Question

Prove that lower limit topology on r is strictly finer than standard topology

Answer 1

Choose c between the two points, then (A ∩ (-∞, c)) ∪ (A ∩ [c, ∞)) is a separation of A in the lower limit topology. ... 7.2.6 A separation in a coarser topology is still a separation in a finer topology. Therefore a coarser topology is not connected implies a finer topology is not connected..............................