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arXiv · 2610.25573

Goldbach and Alexandroff Shake Hands

Lourival Lima·Jorge Vielma
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Abstract

We introduce a relational Alexandroff topology associated with the strong Goldbach conjecture on the set of even integers greater than or equal to six. The construction is induced by a multivalued map encoding Goldbach representations and leads naturally to a notion of relational reachability. For arbitrary binary relations, we show that singleton closures coincide with reachable sets and that the common intersection of all singleton closures consists exactly of the globally reachable points. In the Goldbach setting, this yields a topological characterization of the conjecture in terms of the distinguished point \(6\). In particular, the strong Goldbach conjecture is equivalent to the associated relational space being non-\(wR_0\) and connected. We also obtain compactness and supercompactness criteria in terms of the set of possible Goldbach exceptions.

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Lourival Lima, Jorge Vielma. 2026-10-18. Goldbach and Alexandroff Shake Hands. https://arxiv.org/abs/2610.25573

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