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Q40Section B (Part B)40 of 120

Homeomorphisms of a five-point space with topology {∅,{1},S}\{\emptyset,\{1\},S\}

Let S={1,2,3,4,5}S=\{1,2,3,4,5\} be equipped with the topology τ={∅,{1},S}\tau=\{\emptyset,\{1\},S\}. What is the number of homeomorphisms of SS onto itself?

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