Definition:Point of Locale/Continuous Map

Definition

Let $\struct{L, \preceq}$ be a locale.

A point of $L$ is a continuous map $f: 2 \to \mathbf L$, where $\struct{\mathbf 2, \vee, \wedge, \neg, \preceq}$ denotes the (Boolean lattice) two.

Also see

• Definition:Spectrum of Locale as Continuous Maps

Sources

• 1982: Peter T. Johnstone: Stone Spaces: Chapter $\text {II}$: Introduction to Locales, $\S 1$ Frames and locales, Definition $1.3$