Modularity, atomicity and states in Archimedean lattice effect algebras.
Regular and normal quantales
Conjunctivity in quantales
Note on dense covers in the category of locales
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.
-separation axioms on frames
A note on the prime ideal theorem
Linear finitely separated objects of subcategories of domains
-frames and almost compact frames
Semiregular frames
On some notions related to compactness for locales
A note on extremally disconnected frames
Professor Rosický sexagenarian
Atomicity of lattice effect algebras and their sub-lattice effect algebras
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...
Almost orthogonality and Hausdorff interval topologies of atomic lattice effect algebras
We prove that the interval topology of an Archimedean atomic lattice effect algebra is Hausdorff whenever the set of all atoms of is almost orthogonal. In such a case is order continuous. If moreover is complete then order convergence of nets of elements of 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 corresponding to compact and cocompact elements....
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