  We prove that the interval topology of an Archimedean atomic lattice effect
algebra $E$ is Hausdorff whenever the set of all atoms of $E$ is almost
orthogonal. In such a case $E$ is order continuous. If moreover $E$ is complete
then order convergence of nets of elements of $E$ is topological and hence it
coincides with convergence in the order topology and this topology is compact
Hausdorff compatible with a uniformity induced by a separating function family
on $E$ corresponding to compact and cocompact elements. For block-finite
Archimedean atomic lattice effect algebras the equivalence of almost
orthogonality and s-compact generation is shown. As the main application we
obtain the state smearing theorem for these effect algebras, as well as the
continuity of $\oplus$-operation in the order and interval topologies on them.
