English

On infinite variants of De Morgan law in locale theory

General Topology 2020-08-04 v1 Category Theory Logic

Abstract

A locale, being a complete Heyting algebra, satisfies De Morgan law (ab)=ab(a\vee b)^*=a^*\wedge b^* for pseudocomplements. The dual De Morgan law (ab)=ab(a\wedge b)^*={a^* \vee b^*} (here referred to as the second De Morgan law) is equivalent to, among other conditions, (ab)=ab(a\vee b)^{**} =a^{**}\vee b^{**}, and characterizes the class of extremally disconnected locales. This paper presents a study of the subclasses of extremally disconnected locales determined by the infinite versions of the second De Morgan law and its equivalents.

Keywords

Cite

@article{arxiv.2001.09143,
  title  = {On infinite variants of De Morgan law in locale theory},
  author = {Igor Arrieta},
  journal= {arXiv preprint arXiv:2001.09143},
  year   = {2020}
}