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Arithmetic topology is an area of mathematics that is a combination of algebraic number theory and topology. It establishes an analogy between number fields and closed, orientable 3-manifolds.
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Is Mazur's analogy between arithmetic and topology formal, in any sense?
For this analogy, like most analogies in mathematics, and indeed like most philosophical principles in mathematics, one can certainly make a part of it formal and rigorous, but I don't think any true …