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Akhilesh posted an Question
February 25, 2022 • 09:02 am 30 points
  • IIT JAM
  • Mathematics (MA)

Exercise 3.3.38 (lower limit topology). set b-{la,b): a,be r}. 70 3. topological spaces the topology generated by b is called the lower limit topology and it is

Exercise 3.3.38 (Lower Limit Topology). Set B-{la,b): a,bE R}. 70 3. TOPOLOGICAL SPACES The topology generated by B is called the lower limit topology and it is denoted by R (it is called in some references the Sorgenfrey Topology). (1) Check that B is in effect a base for R. (2) Show that R is strictly coarser than Rg. (3) Give examples of closed, open and clopen sets in R. What is the nature of (a, b]? (4) Is Re Hausdorff? (5) Is Re separable? REMAD Lilrouige H7O matr dofna a tonalnau on P 1sima the hase

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