Definition:Point of Locale/Frame Homomorphism

Definition

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

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

Also see

• Definition:Spectrum of Locale as Frame Homomorphisms

Sources

• 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter $\text {II}$: Spaces and Lattices of Open Sets, $\S 3$ Points, Definition $3.2$