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
Disclosure statement
No potential conflict of interest was reported by the author(s).