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.;
2021-01-01
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.File in questo prodotto:
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