Metric Spaces aren't Torsors

David Wilding

Frank Adams 1,

But (you might reasonably ask) was there any danger of them being torsors in the first place? Actually, you are probably just wondering what a 'torsor' is. A torsor is essentially a group, except we have "forgotten" which element is the identity element. Given a torsor for the additive group of real numbers, we can define a distance function on the torsor that satisfies all but one of the metric space axioms. This suggests that torsors generalise metric spaces, but it turns out that a torsor can never be a metric space. Instead, metric spaces and torsors have a common generalisation, which I will describe

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