Frink ideal topology of lattice effect algebras

A difficult question arising in the study of effect algebras is how to equip them with a fitting and proper topology such that the topology is compatible with the partial operations ⊕ and Θ. As we know, the Frink ideal topology is an important intrinsic topology for studying partially ordered set theory; in particular, it is the correct topology for chains and direct products of a finite number of chains. In this paper, we show that the Frink ideal topology is also a nice topology for studying effect-algebra theory since it provides the operations with some of the expected continuity properties.