Presenting de Groot duality of stably compact spaces

Autor:	Kawai, Tatsuji
Rok vydání:	2018
Předmět:	Computer Science - Logic in Computer Science Mathematics - General Topology 06B35 06D22 03B70 03F60
Druh dokumentu:	Working Paper
Popis:	We give a constructive account of the de Groot duality of stably compact spaces in the setting of strong proximity lattice, a point-free representation of a stably compact space. To this end, we introduce a notion of strong continuous entailment relation, which can be thought of as a presentation of a strong proximity lattice by generators and relations. The new notion allows us to identify de Groot duals of stably compact spaces by analysing the duals of their presentations. We carry out a number of constructions on strong proximity lattices using strong continuous entailment relations and study their de Groot duals. The examples include various powerlocales, patch topology, and the space of valuations. These examples illustrate the simplicity of our approach by which we can reason about the de Groot duality of stably compact spaces. Comment: Fixed some typos
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1812.06480 Zobrazit plný text záznamu View this record from Arxiv