The Golomb space ℕT is the set N of positive integers endowed with the topology T generated by the base consisting of arithmetic progressions {a + bn: n ≥ 0} with coprime a, b. We prove that the Golomb space ℕT is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.

The Golomb space is topologically rigid

Spirito D.;
2021

Abstract

The Golomb space ℕT is the set N of positive integers endowed with the topology T generated by the base consisting of arithmetic progressions {a + bn: n ≥ 0} with coprime a, b. We prove that the Golomb space ℕT is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11390/1216596
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