Variants of Booleanness: Congruences of a partial frame versus those of its free frame
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John Frith
and
Anneliese Schauerte
Abstract
This paper concerns notions of Booleanness in the setting of partial frames, which, in contrast to full frames, do not necessarily have all joins. Examples of these include bounded distributive lattices, σ- and κ-frames. We provide four distinct conditions which all reduce in the case of full frames to each element having a complement. These concepts depend heavily on the free frame over a partial frame, the congruence frame of a partial frame and the relations between them. We also examine the adjoint situation between the congruences of a partial frame and those of its free frame.
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( (Communicated by Anatolij Dvurečenski )
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Articles in the same Issue
- Regular Papers
- Variants of Booleanness: Congruences of a partial frame versus those of its free frame
- Models, coproducts and exchangeability: Notes on states on Baire functions
- Inverse tangent series involving pell and pell-lucas polynomials
- A new family of two-variable polynomials based on hermite polynomials
- Decreasing property and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function
- On the solvability of a fourth-order differential evolution equation on singular cylindrical domain in R4
- Investigation of an implicit Hadamard fractional differential equation with Riemann-Stieltjes integral boundary condition
- Stability criteria for systems of two first-order linear ordinary differential equations
- A perturbed eigenvalue problem in exterior domain
- On extensions of bilinear maps
- Refinement of seminorm and numerical radius inequalities of semi-Hilbertian space operators
- Weighted composition operators from the Besov space into nth weighted type spaces
- Fuzzy ideal topological vector spaces
- Partial actions on convergence spaces
- On quasi-small loop groups
- Topologies generated by symmetric porosity on normed spaces
- The Alpha Power Rayleigh-G family of distributions
- An alternative for Laplace Birnbaum-Saunders distribution
- Existence of positive solutions for boundary value problems with p-Laplacian operator
