On infinite variants of De Morgan law in locale theory

Igor Arrieta Torres

doi:10.1016/j.jpaa.2020.106460

On infinite variants of De Morgan law in locale theory

Igor Arrieta Torres^*

^*Corresponding author for this work

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

A locale, being a complete Heyting algebra, satisfies De Morgan law (a ∨ b)^*= a^* ∧ b^* for pseudocomplements. The dual De Morgan law (a ∧ b)^*= a^* ∨ b^*(here referred to as the second De Morgan law) is equivalent to, among other conditions, (a ∨ b)^**= a^** ∨ 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.

Original language	English
Article number	106460
Number of pages	17
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	1
Early online date	17 Jun 2020
DOIs	https://doi.org/10.1016/j.jpaa.2020.106460
Publication status	Published - Jan 2021

Keywords

Locale
Frame
Sublocale
Booleanization
De Morgan law
Extremal disconnectedness

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abstract = "A locale, being a complete Heyting algebra, satisfies De Morgan law (a ∨ b)* = a* ∧ b* for pseudocomplements. The dual De Morgan law (a ∧ b)* = a* ∨ b* (here referred to as the second De Morgan law) is equivalent to, among other conditions, (a ∨ b)** = a** ∨ 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. ",

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KW - Frame

KW - Sublocale

KW - Booleanization

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On infinite variants of De Morgan law in locale theory

Abstract

Keywords

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