# Topological representation for monadic implication algebras

Abad Manuel; Cimadamore Cecilia; Díaz Varela José

Open Mathematics (2009)

- Volume: 7, Issue: 2, page 299-309
- ISSN: 2391-5455

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topAbad Manuel, Cimadamore Cecilia, and Díaz Varela José. "Topological representation for monadic implication algebras." Open Mathematics 7.2 (2009): 299-309. <http://eudml.org/doc/269669>.

@article{AbadManuel2009,

abstract = {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.},

author = {Abad Manuel, Cimadamore Cecilia, Díaz Varela José},

journal = {Open Mathematics},

keywords = {Implication algebra; Monadic Boolean algebra; Implication spaces; Dual categorical equivalence; implication algebra; monadic implication algebra; topology; implication space; categorical equivalence},

language = {eng},

number = {2},

pages = {299-309},

title = {Topological representation for monadic implication algebras},

url = {http://eudml.org/doc/269669},

volume = {7},

year = {2009},

}

TY - JOUR

AU - Abad Manuel

AU - Cimadamore Cecilia

AU - Díaz Varela José

TI - Topological representation for monadic implication algebras

JO - Open Mathematics

PY - 2009

VL - 7

IS - 2

SP - 299

EP - 309

AB - 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.

LA - eng

KW - Implication algebra; Monadic Boolean algebra; Implication spaces; Dual categorical equivalence; implication algebra; monadic implication algebra; topology; implication space; categorical equivalence

UR - http://eudml.org/doc/269669

ER -

## References

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- [9] Halmos P.R., Algebraic logic, Chelsea Publishing Co., New York, 1962
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- [11] Koppelberg S., Handbook of Boolean algebras, North-Holland Publishing Co., Amsterdam, 1989

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