### Conjunctivity in quantales

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In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.

We show some families of lattice effect algebras (a common generalization of orthomodular lattices and MV-effect algebras) each element E of which has atomic center C(E) or the subset S(E) of all sharp elements, resp. the center of compatibility B(E) or every block M of E. The atomicity of E or its sub-lattice effect algebras C(E), S(E), B(E) and blocks M of E is very useful equipment for the investigations of its algebraic and topological properties, the existence or smearing of states on E, questions...

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....

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