L. Peter Belluce, Antonio Di Nola
Frames and MV-Algebras
Preprint series: ESI preprints

MSC:

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces, See also {46A40}

06F25 Ordered rings, algebras, modules, {For ordered fields, See

06D30 De Morgan algebras, Lukasiewicz algebras, See also {03G20}

Abstract: This is a preliminary study of 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 $Hom_{\cal F}(\Omega (A), \ {\bf K})$ in the category
$\cal F$ of frames, where $A$ is a topological MV-algebra,
$\Omega(A)$ the lattice of open sets of $A$, and ${\bf K}$ an
arbitrary frame.\par 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 ${\bf K}$
is spatial, then ${\cal C}(pt({\bf K}), A),\ pt({\bf K})$ the
points of ${\bf K}$, embeds into $Hom_{\cal F}(\Omega(A), {\bf
K})$ analogous to the case of ${\cal C}(X, A)$ embedding into
$Hom_{\cal F}(\Omega(A), \Omega(X))$.
Keywords: MV-algebra, frame