In this paper, we prove that if $\mathcal{A}=\{E_i\}_{i=1}^{n}$ is a finite
commutative quantum measurement, then the fixed points set of L\"{u}ders
operation $L_{{\cal A}}$ is the commutant ${\cal A}'$ of ${\cal A}$, the result
answers an open problem partially. We also give a concrete example of a
L\"{u}ders operation $L_{{\cal A}}$ with $n=3$ such that $L_{{\cal A}}(B)=B$
does not imply that the quantum effect $B$ commutes with all $E_1, E_2$ and
$E_3$, this example answers another open problem.

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.