Boolean differential operators
We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.
We consider four combinatorial interpretations for the algebra of Boolean differential operators and construct, for each interpretation, a matrix representation for the algebra of Boolean differential operators.
∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions on the corresponding...
In this note results obtained by S.Ray (1997) on representation of a Boolean algebra by its triangular norms are generalized.
Booleanization of frames or uniform frames, which is not functorial under the basic choice of morphisms, becomes functorial in the categories with weakly open homomorphisms or weakly open uniform homomorphisms. Then, the construction becomes a reflection. In the uniform case, moreover, it also has a left adjoint. In connection with this, certain dual equivalences concerning uniform spaces and uniform frames arise.