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.

中文翻译：

---

论地域理论中德摩根定律的无限变体

摘要 语言环境是一个完整的 Heyting 代数，对于伪补码，它满足德摩根定律 (a ∨ b ) ⁎ = a ⁎ ∧ b ⁎。对偶德摩根定律 ( a ∧ b ) ⁎ = a ⁎ ∨ b ⁎（这里称为第二德摩根定律）等价于，除其他条件外， ( a ∨ b ) ⁎ ⁎ = a ⁎ ⁎ ∨ b ⁎ ⁎ ，并表征了极不连接的语言环境的类别。本文介绍了由第二德摩根定律及其等价物的无限版本确定的极不连接区域的子类的研究。