Weakly algebraic ideal topology of effect algebras

In this paper, we show that every weakly algebraic ideal of an effect algebra E induces a uniform topology (weakly algebraic ideal topology, for short) with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation . of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation . of effect algebras and the operations . and . of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.