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A Priestley Sum of Finite Trees is Acyclic

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Abstract

We show that the Priestley sum of finite trees contains no cyclic finite poset.

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References

  1. Ball, R.N., Pultr, A.: Forbidden forests in Priestley spaces. Cahiers Topologie Géom. Différentielle Catég. XLV-1, 2–22 (2004)

    MathSciNet  Google Scholar 

  2. Ball, R.N., Pultr, A., Sichler, J.: Priestley configurations and Heyting varieties. (to appear in Algebra Universalis)

  3. Ball, R.N., Pultr, A., Sichler, J.: Configurations in coproducts of priestley spaces. Appl. Categ. Structures 13, 121–130 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ball, R.N., Pultr, A., Sichler, J.: Combinatorial trees in Priestley spaces. Comment. Math. Univ. Carolin. 46, 217–234 (2005)

    MATH  MathSciNet  Google Scholar 

  5. Ball, R.N., Pultr, A., Sichler, J.: The mysterious 2-crown. Algebra Universalis 55, 213–226 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order, 2nd Edn., Cambridge University Press (2001)

  7. Koubek, V., Sichler, J.: On priestley duals of products. Cahiers Topologie Géom. Différentielle Catég. XXXII, 243–256 (1991)

    MathSciNet  Google Scholar 

  8. Priestley, H.A.: Representation of distributive lattices by means of ordered Stone spaces. Bull. London Math. Soc. 2, 186–190 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  9. Priestley, H.A.: Ordered topological spaces and the representation of distributive lattices. Proc. London Math. Soc. 324, 507–530 (1972)

    Article  MathSciNet  Google Scholar 

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Correspondence to Aleš Pultr.

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The first author would like to express his thanks for support from project LN 1M0021620808 of the Ministry of Education of the Czech Republic. The second author would like to express his thanks for support from project 1M0021620808 of the Ministry of Education of the Czech Republic, from the NSERC of Canada and from a PROF grant from the University of Denver. The third author would like to express his thanks for the support from the NSERC of Canada and for partial support from the project 1M0021620808 of the Ministry of Education of the Czech Republic.

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Ball, R.N., Pultr, A. & Sichler, J. A Priestley Sum of Finite Trees is Acyclic. Appl Categor Struct 16, 735–748 (2008). https://doi.org/10.1007/s10485-007-9118-z

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  • DOI: https://doi.org/10.1007/s10485-007-9118-z

Keywords

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