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The Golomb space is topologically rigid

Taras O. Banakh, Dario Spirito, Sławomir Turek (2021)

Commentationes Mathematicae Universitatis Carolinae

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

Triangular repunit-there is but 1

John H. Jaroma (2010)

Czechoslovak Mathematical Journal

In this paper, we demonstrate that 1 is the only integer that is both triangular and a repunit.

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