Interval convexity of scale effect algebras

Abstract

In this paper, we first propose the concept of DC-nets, where its domain is a DCPO, in convexity spaces and discuss some related properties. And then, we obtain that is convexity-preserving if and only if converges to f(a) with respect to when converges to a with respect to Hence, we could discuss convexity-preserving properties of partial binary operations + and – of effect algebras by convergence of DC-nets in convexity spaces. Concretely, we prove that if is a scale effect algebra and is an interval convexity on E, then + and – are separately convexity-preserving with respect to . Finally, we provide an example to show that + and – are not jointly convexity-preserving with respect to when is a lattice effect algebra. Communicated by Ángel del Río Mateos