There is no categorical metric continuum
General Topology
2007-05-23 v2 Logic
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.
Cite
@article{arxiv.math/0509099,
title = {There is no categorical metric continuum},
author = {Klaas Pieter Hart},
journal= {arXiv preprint arXiv:math/0509099},
year = {2007}
}
Comments
Revision after comments from referee (2006-01-16)