On infinite variants of De Morgan law in locale theory
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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