Abstract
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.
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