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The semigroup of increasing functions on the rational numbers has a unique Polish topology

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arxiv 2305.04921 v2 pith:2YWU4NDI submitted 2023-05-08 math.RA math.GN

classification math.RAmath.GN
keywords functionsincreasingsemigrouptopologynumberspolishrationaltechniques
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The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions converges if and only if it is eventually constant at every argument. We develop new techniques to prove there is no other Polish topology turning this semigroup into a topological one, and show that previous techniques are insufficient for this matter.

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Cited by 2 Pith papers

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