Locally Compact Stone Duality
General Topology
2019-11-19 v2 Logic
Abstract
We prove a number of dualities between posets and (pseudo)bases of open sets in locally compact Hausdorff spaces. In particular, we show that (1) Relatively compact basic sublattices are finitely axiomatizable. (2) Relatively compact basic subsemilattices are those omitting certain types. (3) Compact clopen pseudobasic posets are characterized by separativity. We also show how to obtain the tight spectrum of a poset as the Stone space of a generalized Boolean algebra that is universal for tight representations.
Cite
@article{arxiv.1609.09708,
title = {Locally Compact Stone Duality},
author = {Tristan Bice and Charles Starling},
journal= {arXiv preprint arXiv:1609.09708},
year = {2019}
}
Comments
Introduction reorganized and some references added