A topological duality for strong Boolean posets
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Zhenzhu Yuan
Abstract
In this paper, we define a new class of posets which are complemented and ideal-distributive, we call these posets strong Boolean. This definition is a generalization of Boolean lattices on posets, and is different from Boolean posets. We give a topology on the set of all prime Frink ideals in order to obtain the Stone’s topological representation for strong Boolean posets. A discussion of a duality between the categories of strong Boolean posets and BP-spaces is also presented.
(Communicated by Anatolij Dvurečenskij)
Acknowledgement
We would like to express our deep gratitude to the referee for his/her invaluable comments which have improved the quality of this paper.
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© 2019 Mathematical Institute Slovak Academy of Sciences
Artikel in diesem Heft
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
Artikel in diesem Heft
- Regular papers
- The life jubilee of Prof. RNDr. Sylvia Pulmannová, DrSc.
- Perfect 1-factorizations
- A topological duality for strong Boolean posets
- On the Diophantine equations x2 + 2α 3β 19γ = yn and x2 + 2α 3β 13γ = yn
- Tribonacci numbers and primes of the form p = x2 + 11y2
- Basic semirings
- A conjecture for varieties of completely regular semigroups
- Uniqueness of meromorphic function with its shift operator under the purview of two or three shared sets
- Differential subordination results for Mittag-Leffler type functions with bounded turning property
- Mittag-Leffler stability for non-instantaneous impulsive Caputo fractional differential equations with delays
- Asymptotically periodic behavior of solutions of fractional evolution equations of order 1 < α < 2
- On the polynomial entropy for morse gradient systems
- Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators
- A note on non-linear ∗-Jordan derivations on ∗-algebras
- Disjoint hypercyclic weighted translations on locally compact hausdorff spaces
- Some new results on real hypersurfaces with generalized Tanaka-Webster connection
- Relative topological properties of hyperspaces
- Cohomology of torus manifold bundles
- The Menger and projective Menger properties of function spaces with the set-open topology
- Asymptotic behavior of the record values in a stationary Gaussian sequence, with applications
