Question: Topology help!!! 9:20 1 For each n E N, let Bn = {n, n + 1, n + 2, . .. } and B =

Topology help!!!

9:20 1 For each n E N, let Bn = {n, n + 1, n + 2, . .. } and B = {Bn : n E N}. a. Show that B is a basis for a topology on N. b. Prove that every sequence (of natural numbers) in which no element repeats more than finitely many times converges to every natural number in this topology. c. Find a sequence (of natural numbers) with infinite range that converges only to 1 in this topology. d. Which of the following properties does this topological space possess? Justify your answers. Hausdorff, first countable, second countable, separable, Lindelof, connected, compact

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