# 完全海廷代数

## 定义

• P是海廷代数，就是说运算 ( x ${\displaystyle \wedge }$  - )有一个右伴随（也叫做（单调）伽罗瓦连接的下伴随），对于每个P的元素x
• 对于所有P的元素x和所有P的子集S，下列无限分配律成立：
${\displaystyle x\wedge \bigvee S=\bigvee \{x\wedge s\mid s\in S\}}$
• P是分配格，就是说对于所有P中的x, yz，有着
${\displaystyle x\wedge (y\vee z)=(x\wedge y)\vee (x\wedge z)}$

## 引用

• P. T. Johnstone, Stone Spaces, Cambridge Studies in Advanced Mathematics 3, Cambridge University Press, Cambridge, 1982. (ISBN 0-521-23893-5)
Still a great resource on locales and complete Heyting algebras.
• G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, and D. S. Scott, Continuous Lattices and Domains, In Encyclopedia of Mathematics and its Applications, Vol. 93, Cambridge University Press, 2003. ISBN 0-521-80338-1
Includes the characterization in terms of meet continuity.
• Francis Borceux: Handbook of Categorical Algebra III, volume 52 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1994.
Surprisingly extensive resource on locales and Heyting algebras. Takes a more categorical viewpoint.