On additive involutions and Hamel bases |
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Authors: | Karol Baron |
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Institution: | 1. Instytut Matematyki, Uniwersytet ?la?ski, ul. Bankowa 14, 40-007, Katowice, Poland
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Abstract: | We provide an example of a discontinuous involutory additive function ${a: \mathbb{R}\to \mathbb{R}}$ such that ${a(H) \setminus H \ne \emptyset}$ for every Hamel basis ${H \subset \mathbb{R}}$ and show that, in fact, the set of all such functions is dense in the topological vector space of all additive functions from ${\mathbb{R}}$ to ${\mathbb{R}}$ with the Tychonoff topology induced by ${\mathbb{R}^{\mathbb{R}}}$ . |
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