Sergio Zamora
Abstract
Here we obtain upper bounds for diameters of covering spaces of compact length spaces with the lifted metric. We give a proof by Sergei Ivanov of the fact that the diameter of an $n$-fold cover of a space of diameter $d$ is bounded above by $dn$. We also show that the bound can be improved to $4d\sqrt{n}$ if the cover is universal.
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Here we obtain upper bounds for diameters of covering spaces of compact length spaces with the lifted metric. We give a proof by Sergei Ivanov of the fact that the diameter of an $n$-fold cover of a space of diameter $d$ is bounded above by $dn$. We also show that the bound can be improved to $4d\sqrt{n}$ if the cover is universal.
Key concepts: Cover (algebra), Covering space, Bounded function, Mathematics, Metric space, Upper and lower bounds, Metric (unit), Combinatorics