Order Topology and Frink Ideal Topology of Effect Algebras

In this paper, the following results are proved: (1) If E is a complete atomic lattice effect algebra, then E is (o)-continuous iff E is order-topological iff E is totally order-disconnected iff E is algebraic. (2) If E is a complete atomic distributive lattice effect algebra, then its Frink ideal topology τ _id is Hausdorff topology and τ _id is finer than its order topology τ _o , and τ _id = τ _o iff 1 is finite iff every element of E is finite iff τ _id and τ _o are both discrete topologies. (3) If E is a complete (o)-continuous lattice effect algebra and the operation ⊕ is order topology τ _o continuous, then its order topology τ _o is Hausdorff topology. (4) If E is a (o)-continuous complete atomic lattice effect algebra, then ⊕ is order topology continuous.