Topological representation for monadic implication algebras

In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implicatio...

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Bibliographic Details
Published in:Central European journal of mathematics 2009, Vol.7 (2), p.299-309
Main Authors: Abad, Manuel, Cimadamore, Cecilia Rossana, Díaz Varela, José Patricio
Format: Article
Language:English
Subjects:
03G25
06E15
06F99
Algebra
Boolean algebra
Dual categorical equivalence
Geometry
Implication algebra
Implication spaces
Lie Groups
Mathematics
Mathematics and Statistics
Monadic Boolean algebra
Number Theory
Probability Theory and Stochastic Processes
Representations
Research Article
Topological Groups
Topology
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Summary:In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
ISSN:1895-1074
2391-5455
1644-3616
2391-5455
DOI:10.2478/s11533-009-0002-y