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An Illustration of the Power of Structure Theory

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Abstract

There is a hierarchy of concepts of compact semigroups according to the degree of continuity of their multiplications: One-sided continuity, separate continuity, continuity. Each level of generality has its own fields of application and its own peculiarities. This is illustrated in a discussion of three seemingly rather unrelated examples from different branches of mathematics: number theory, functional analysis, logic.

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References

  1. Ellis, R.: Distal transformation groups, Pacific J. Math. 8(1958), 401–405.

    Google Scholar 

  2. Gierz, G., Hofmann, K. H., Keimel, K., Lawson, J. D., Mislove, M. W., and Scott, D. S.: A Compendium of Continuous Lattices, Springer-Verlag, Heidelberg, 1980.

    Google Scholar 

  3. Hindman, N.: The semigroup_N and its applications to number theory, in K. H. Hofmann, J. D. Lawson, and J. S. Pym (eds), The Analytical and Topological Theory of Semigroups, De Gruyter, Berlin, 1990, pp. 347–360.

    Google Scholar 

  4. Hindman, N. and Papert, D.: Algebra in the Stone-Čech Compactification, De Gruyter, Berlin, 1998.

    Google Scholar 

  5. Hofmann, K. H. and Mislove, M. W.: All compact Hausdorff models are degenerate, Fund. Inform. 22(1995), 23–52.

    Google Scholar 

  6. Hofmann, K. H. and Mislove, M. W.: Principles underlying the degeneracy of topological models of the untyped lambda calculus, in K. H. Hofmann and M.W. Mislove (eds), Semigroup Theory and Its Applications, Cambridge Univ. Press, 1996, pp. 123–155.

  7. Hofmann, K. H. and Mostert, P. S.: Elements of Compact Semigroups, Charles E. Merrill Publishers, Columbus, OH, 1966.

    Google Scholar 

  8. Lawson, J. D.: A purely semigroup theoretical proof of van der Waerden's Theorem, Personal Communication, December 1995.

  9. Mislove, M. W.: Topology, domain theory, and theoretical computer science, Elsevier Preprint, September 1996.

  10. Haase, M.: Ramsey Theorie und die Stone-Čech-Kompaktifizierung diskreter Halbgruppen, Diplom Thesis, University of Tübingen, 1997.

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  1. Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, D-64289, Darmstadt, Germany

    Karl H. Hofmann

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  1. Karl H. Hofmann
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Hofmann, K.H. An Illustration of the Power of Structure Theory. Applied Categorical Structures 8, 145–160 (2000). https://doi.org/10.1023/A:1008655708680

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  • DOI: https://doi.org/10.1023/A:1008655708680

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