Inverse semigroup of metrics on a double is fundamental

We show that the inverse group of equivalence classes of metrics on two copies of a metric space is fundamental.

💡 Research Summary

The paper studies the algebraic structure of equivalence classes of metrics defined on the double of a metric space. Given a metric space (X), its double is the product (X\times{0,1}) equipped with a metric that coincides with the original metric on each copy and assigns a strictly positive distance between the two copies. Two such metrics are considered coarsely equivalent if there exists a homeomorphism (\varphi: