Frames and MV-algebras

Abstract

We describe a class of MV-algebras which is a natural generalization of the class of “algebras of continuous functions”. More specifically, we're interested in the algebra of frame maps Hom ${_{\cal F}}$ (Ω(A), K) in the category T of frames, where A is a topological MV-algebra, Ω(A) the lattice of open sets of A, and K an arbitrary frame.

Given a topological space X and a topological MV-algebra A, we have the algebra C (X, A) of continuous functions from X to A. We can look at this from a frame point of view. Among others we have the result: if K is spatial, then C(pt(K), A), pt(K) the points of K, embeds into Hom ${_{\cal F}}$ (Ω(A), K) analogous to the case of C (X, A) embedding into Hom ${_{\cal F}}$ (Ω(A), Ω (X)).