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Compact Hausdorff Heyting algebras

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Abstract

We prove that the topology of a compact Hausdorff topological Heyting algebra is a Stone topology. It then follows from known results that a Heyting algebra is profinite iff it admits a compact Hausdorff topology that makes it a compact Hausdorff topological Heyting algebra.

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References

  1. Bezhanishvili G., Bezhanishvili N.: Profinite Heyting algebras. Order 25, 211–227 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bezhanishvili, G., Harding, J.: On the proof that compact Hausdorff Boolean algebras are powersets. Order (to appear), DOI 10.1007/s11083-015-9363-y

  3. Johnstone P. T.: Stone spaces. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  4. Numakura K.: Theorems on compact totally disconnected semigroups and lattices. Proc. Amer. Math. Soc. 8, 623–626 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  5. Papert Strauss D.: Topological lattices. Proc. London Math. Soc. 18, 217–230 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  6. Rasiowa H., Sikorski R.: The Mathematics of metamathematics. Państwowe Wydawnictwo Naukowe, Warsaw (1963)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    Guram Bezhanishvili & John Harding

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  1. Guram Bezhanishvili
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  2. John Harding
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Correspondence to Guram Bezhanishvili.

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Bezhanishvili, G., Harding, J. Compact Hausdorff Heyting algebras. Algebra Univers. 76, 301–304 (2016). https://doi.org/10.1007/s00012-016-0387-y

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  • DOI: https://doi.org/10.1007/s00012-016-0387-y

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