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There is no categorical metric continuum

Klaas Pieter Hart
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Abstract

We show there is no categorical metric continuum. This means that for every metric continuum X there is another metric continuum Y such that X and Y have (countable) elementarily equivalent bases but X and Y are not homeomorphic. As an application we show that the chainability of the pseudoarc is not a first-order property of its lattice of closed sets.

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Klaas Pieter Hart. 2006-01-16. There is no categorical metric continuum. https://arxiv.org/abs/math/0509099

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