Sierpiński Index of Classical Transformation Semigroups
نویسنده
چکیده
We prove that any countable set of surjective functions on an infinite set of cardinality אn with n ∈ N can be generated by at most n2/2 + 9n/2 + 5 surjective functions of the same set; and there exist n2/2 + 9n/2 + 5 surjective functions that cannot be generated by any smaller number of surjections. If injective functions are considered instead of surjective functions, then n + 4 replaces n2/2 + 9n/2 + 5. We present several analogous results for other classical infinite transformation semigroups.
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تاریخ انتشار 2010