User:Leigh.Samphier/CategoryTheory/Definition:Frame of Open Sets Functor

Definition

Let $\mathbf{Top}$ denote the category of topological spaces.

Let $\mathbf{Frm}$ denote the category of frames.

The (frame of) open sets functor, denoted $\mathbf \Omega : \mathbf{Top} \to \mathbf{Frm}$, is the contravariant functor defined by:

			Object functor:					$\map \Omega T := $ the frame of topological space $T$
			Morphism functor:					$\map \Omega f := $ the frame homomorphism of continuous mapping $f$

Also see

• User:Leigh.Samphier/CategoryTheory/Frame of Open Sets Functor is Contravariant

Sources

• 2012: Jorge Picado and Aleš Pultr: Frames and Locales: Chapter II: Frames and Locales. Spectra, $\S 1.3$