Grothendieck topologies on posets
Abstract
Lindenhovius has studied Grothendieck topologies on posets and has given a complete classification in the case that the poset is Artinian. We extend his approach to more general posets, by translating known results in locale and domain theory to the study of Grothendieck topologies. In particular, explicit descriptions are given for the family of Grothendieck topologies with enough points and the family of Grothendieck topologies of finite type. As an application, we compute the cardinalities of these families in various examples.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 arXiv:
 arXiv:1811.10039
 Bibcode:
 2018arXiv181110039H
 Keywords:

 Mathematics  Category Theory;
 Mathematics  Algebraic Geometry;
 Mathematics  General Topology;
 Mathematics  Logic
 EPrint:
 16 pages