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

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

Michael Pinsker , Clemens Schindler This is my paper

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classification math.RA math.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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Polish topologies on endomorphism monoids of linear orders

    math.GR 2026-05 unverdicted novelty 6.0

    Authors introduce property XX for automatic continuity and prove that End^∞(N,≤) has a unique Polish semigroup topology while End(N,≤), End(Z,≤) have infinitely many and End(N,<) has continuum many.