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arXiv · 2606.08384

Discontinuous homomophisms without Hamel bases

Paul Larson·Saharon Shelah
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Abstract

We produce a model of ZF + DC in which there exists a discontinuous homomorphism from the real line to itself but no Hamel basis for the real line, and prove a generalization of this result in terms of internal direct sums.

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Paul Larson, Saharon Shelah. 2026-06-07. Discontinuous homomophisms without Hamel bases. https://arxiv.org/abs/2606.08384

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