Interval topology of lattice effect algebras

Let ( E , ⊥ , ⊕ , 0 , 1 ) be a lattice effect algebra and τ i its interval topology. In this work we show that if the operation ⊕ is continuous with respect to τ i , then τ i is Hausdorff. In addition, we also show that if ( E , ⊥ , ⊕ , 0 , 1 ) is a complete M V -effect algebra and τ i is a Hausdorff topology, then the operations ⊕ , ⊖ , ∨ and ∧ are τ i continuous.