There is no categorical metric continuum
arXiv:math/0509099
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.
Revision after comments from referee (2006-01-16)