Order Topology and Frink Ideal Topology of Effect Algebras

In this paper we prove the following conclusions: (1). If E is a complete atomic lattice effect algebra, then E is (o)-continuous ⇔ E is order-topological ⇔ E is a totally order-disconnected ⇔ E is algebraic. (2). If E is a complete atomic distributive lattice effect algebra, then its Frink ideal topology τid is Hausdorff topology and is finer than its order topology τo, and τid = τo ⇔ 1 is finite ⇔ every element of E is finite ⇔ τid and τo are both discrete topologies. (3). If E is a complete (o)-continuous lattice effect algebra, then the necessary condition for ⊕ is order topology τo continuous is that τo is Hausdorff topology. (4). If E is a complete atomic lattice effect algebra, then its (o)-continuity can guarantee its order topology continuity of operation ⊕.