Klaus Keimel


Publications

Monographs

  1. A General Character Theory for Partially Ordered Sets and Lattices
    Memoirs Amer. Math. Soc. 122 (1972), 121 pages.
    (joint with K.H.Hofmann.)

  2. Groupes et Anneaux Réticulés
    Lecture Notes in Mathematics, 608 (1977), Springer Verlag, xiv+334 pages.
    (joint with A.Bigard and S.Wolfenstein.) [Electronic Access]

  3. A Compendium of Continuous Lattices
    Springer Verlag, 1980, xx+371 pages.
    (joint with G.Gierz, K.H.Hofmann, J.D.Lawson, M.Mislove, and D.S.Scott.)

  4. Ordered Cones and Approximation
    Lecture Notes in Mathematics, 1517 (1992), Springer Verlag, vi+134 pages.
    (joint with W.Roth). [Electronic Access]

  5. Continuous Lattices and Domains
    Encyclopedia of Mathematics and its Applications, vol. 93, Cambridge University Press, 2003, xxxvi+591 pages.
    (joint with G.Gierz, K.H.Hofmann, J.D.Lawson, M.W.Mislove, and D.S.Scott.)

  6. Semantic Domains for Combining Probability and Non-Determinism
    Electronic Notes in Theoretical Computer Science 129 (2005), 104 pages.
    and in slightly modified form 222 (2009), 99 pages (joint with R. Tix and G.D. Plotkin). [PDF]

Articles in Journals and Refereed Proceedings:

  1. Fuseaux généralisés dans la théorie des groupes ordonnés
    C.R. Acad. Sc. Paris 262 (1966), pp. 993-995.

  2. Eine Exponentialfunktion für kompakte abelsche Halbgruppen
    Math. Zeitschrift 96 (1967), pp. 7-25. [PDF]

  3. Lokal kompakte Kegelhalbgruppen und deren Einbettung in topologische Vektorräume
    Math. Zeitschrift, 99 (1967), pp. 405-428. [PDF]

  4. Représentation d'anneaux réticulés dans des faisceaux
    C.R. Acad. Sc. Paris 266 (1968), pp. 124-127.

  5. Anneaux réticulés quasiréguliers et hyperarchimédiens
    C.R. Acad. Sc. Paris 226 (1968), pp. 524-525.

  6. Demi-groupes partiellement ordonnés de deuxième et troisième espèce
    Atti Accad. Naz. Lincei 44 (1968), pp. 21-33.

  7. Le centroide et le bicentroide de certains anneaux réticulés
    C.R. Acad. Sc. Paris 267 (1968), pp. 589-591.

  8. Sur les endomorphismes conservant les polaires d'un groupe réticulé archimédien
    Bull. Soc. Math. France 97 (1969), pp. 381-398, (joint with A. Bigard.) [PDF]

  9. Darstellung von Halbgruppen und universellen Algebren durch Schnitte in Garben; bireguläre Halbgruppen
    Math. Nachrichten 45 (1970), pp. 81-96.

  10. Algèbres commutatives engendrées par leurs éléments idempotents
    Canad. J. Math. 22 (1970), pp. 1071-1078.

  11. A unified theory of minimal prime ideals
    Acta Math. Acad. Sci. Hung. 23 (1972), pp. 51-69.

  12. A cross section theorem for compact abelian semigroups
    Semigroup Forum 1 (1970), pp. 254-259. [PDF]

  13. Baer extensions of rings and Stone extensions of semigroups
    Semigroup Forum 2 (1971), pp. 55-63. [PDF]

  14. Congruence relations on cone semigroups
    Semigroup Forum 3 (1971), pp. 130-147. [PDF]

  15. Radicals in lattice-ordered rings
    Proceedings Coll. Math. Soc. J. Bolyai 6. Rings, Modules, and Radicals 1971, North-Holland, pp. 237-253.

  16. The representation of lattice-ordered groups and rings by sections in sheaves
    In: Lecture Notes on the Applications of Sheaves to Ring Theory, Lecture Notes in Mathematics, 248 (1971), Springer Verlag, pp. 1-98. [ Electronic Access]

  17. Stone duality for varieties generated by quasi-primal algebras
    Memoirs Amer. Math. Soc. 148 (1974), pp. 59-85 (joint with H.Werner).

  18. Representations of lattice-ordered rings
    Proc. Conf. Lattice Theory, Houston (1974), pp. 277-293. [Electronic access], [Entire Proceedings]

  19. A lemma on primes and its appearance in algebra and analysis
    Houston J. Math. 3 (1977), pp. 207-224 (joint with G.Gierz).

  20. Topologische Darstellung von Verbänden
    Math. Zeitschrift 150 (1976), pp. 83-99 (joint with G.Gierz). [PDF]

  21. Positive derivations on f-rings
    J. Austral. Math. Soc., ser. A 23 (1977), pp. 371-375, (joint with P.Colville and G.Davis).

  22. Structure spaces and the center of vector lattices
    Oxford Quarterly J. Math. 29 (1978), pp. 415-426, (joint with H.O.Flösser and G.Gierz).

  23. The semilattices with distinguished endomorphisms which are equationally compact
    Proc. Amer. Math. Soc. 73 (1979), pp. 7-10 (joint with S.Bulman-Fleming and I.Fleischer).

  24. Sheaf theoretical concepts in analysis: Bundles and sheaves of Banach spaces, Banach C(X)-modules
    In: Applications of Sheaves, Lecture Notes in Mathematics, 753 (1979), Springer Verlag,  415-441 (joint with K.H.Hofmann). [ Electronic Access]

  25. Verfeinerungs- und Kürzungssätze für direkte Produkte geordneter topologischer Räume und Funktionen(halb)verbände
    In:  Continuous Lattices, Lecture Notes in Mathematics, 871 (1981), Springer Verlag, pp. 20-44 (joint with H.Bauer and R.Köhler). [Electronic Access]

  26. Continuous ideal completions and compactifications
    ibid., pp. 97-124 (joint with Gierz). [Electronic Access]

  27. Halbstetige Funktionen und stetige Verbände
    In:  Continuous Lattices and Related Topics, Mathematik Arbeitspapiere, 27 (1982), Universität Bremen, pp. 59-67 (joint with G.Gierz). [PDF]

  28. Integral representations of linear functionals on spaces of functions
    Appendix in: G.Gierz:  Bundles of Topological Vector Spaces and their Duality, Lecture Notes in Mathematics 955 (1982), Springer Verlag, pp. 260-283 (joint with G.Gierz).[ Electronic Access]

  29. Kakutani property of the polytopes implies the Kakutani property of the whole space
    J. Math. Analysis Appl. 130 (1988), pp. 97-109, (joint with A. Wieczorek.)

  30. A Korovkin type approximation theorem for set-valued functions
    Proc. Amer. Math. Soc. 104 (1988), pp. 819-824, (joint with W.Roth.)

  31. A direct proof of the Hofmann-Mislove theorem
    Proc. Amer. Math. Soc. 104 (1994), pp. 301-303 (joint with J. Paseka).

  32. Linear Types and Approximation (Extended Abstract)
    Logic in Computer Science, 1994 IEEE Computer Society Press, July 1994, pp. 110-114, (joint with M. Huth and A. Jung).

  33. Some Trends in lattice-ordered groups and rings
    In: Lattice Theory and its Applications (K. A. Baker and R. Wille, eds.), Heldermann Verlag 1995, pp. 131-161.

  34. The way-below relation of function spaces over semantic domains
    Topology and its Applications 89 (1998), pp. 61-74 (joint with Th. Erker and M.H. Escardo). [PS]

  35. Bi-continuous valuations
    Electronic Notes in Theoretical Computer Science 13 (1998), pp. 119-123. [PS]

  36. Compact continuous L-domains
    Computers and Mathematics with Applications 38 (1999), pp. 81-89 (joint with Liang Jihua).

  37. Linear types, approximation, and topology
    Math. Structures in Computer Science 10 (2000), pp. 719-746 (joint with M. Huth and A. Jung).

  38. Order environments of topological spaces
    Acta Mathematica Sinica 20 (2004), pp. 943-948 (joint with Liang Jihua).

  39. The probabilistic powerdomain for stably compact spaces via compact ordered spaces
    Electronic Notes in Theoretical Computer Science 87 (2004), pp. 225--238. [PDF]

  40. Valuations and measures on stably compact spaces
    Theoretical Computer Science 328 (2004), pp. 221--244, (joint with M. Alvarez Manilla and A. Jung). [PDF]

  41. Measure extension theorems for T0-spaces
    Topology and its Applications 149 (2005), pp. 57--83, (joint with J.D. Lawson). [PDF]

  42. Topological cones: Foundations for a domain theoretical Semantics combining probability and nondeterminism
    In: M. Escard¨®, A. Jung and M. Mislove (Eds.), Proceedings of the 21st Annual Conference on Mathematical
    Foundations of Programming Semantics (MFPS XXI), Birmingham, UK, 18-21 May 2005.
    Electronic Notes in Theoretical Computer Science 155 (2006), pp.  423--443. [PDF]

  43. Projective topology on bifinite domains and applications
    Theoretical Computer Science 365 (2006), pp. 171--183 (joint with S. Abbes). [PDF]

  44. The extended probabilistic power domain monad over stably compact spaces
    in: J.-Y. Cai, S.B. Cooper, A. Li (eds), Proceedings of TAMC06: Theory and Applications of Models of Computation, Bejing 2006
    Lecture Notes in Computer Science 3959 (2006), pp.  566--575 (joint with B. Cohen and M. Escardo). [PDF]

  45. Topological Cones: Functional analysis in a T$_0$-setting
    Semigroup Forum 77 (2008), pp. 108--142. [PDF]

  46. The monad of probability measures over compact ordered spaces and its Eilenberg-Moore algebras
    Topology and its Applications 156 (2008), pp. 227--239. [PDF]

  47. Predicate transformers for extended probability and non-determinism
    Mathematical Structures in Computer Science 19 (2009), pp.   501--539 (joint with G. D. Plotkin). [PDF]

  48. D-completions and the d-topology
    Annals of Pure and Applied Logic 159 (2009), pp.  292--306 (joint with J.D.Lawson). [PDF]

  49. A Minkowski type duality mediating between state and predicate transformer semantics for a probabilistic nondeterministic language
    Annals of Pure and Applied Logic 159 (2009), pp.  307--317 (joint with A.Ph. Rosenbusch and Th. Streicher). [PDF]

  50. Abstract ordered compact convex sets and the algebras of the (sub-)probabilistic powerdomain monad over ordered compact spaces
    In Russian: Algebra i Logika 48 (2009), 580--605.
    In English: Algebra and Logic 48 (2009), 330--343. [PDF]

  51. Bicontinuous domains and some old problems in domain theory
    Electronic Notes in Theoretical Computer Science 257   (2009), 35--54. [PDF]

  52. Relating direct and predicate transformer partial correctness semantics for an imperative probabilistic-nondeterministic language
    Theoretical Computer Science 412 (2011),   2701--2713 (joint with A.Ph. Rosenbusch and Th. Streicher). [PDF]

  53. Extending algebraic operations to D-completions
    Electronic Notes in Theoretical Computer Science 249 (2009), 93--116
    Extended version: Theoretical Computer Science  (2011),   to appear (joint with J.D.Lawson). [PDF]

  54. Imprecise probabilities, bets, and functional analytic methods in Lukasiewicz logic
    37 pages,   to appear in: Forum Mathematicum (joint with M. Fedel, F. Montagna and W. Roth). DOI 10.1515/FORM.2011.123 [PDF]

  55. Choquet-Kendall-Matheron theorems for non-Hausdorff spaces
    Mathematical Structures in Computer Science 21   (2011), 511--561 (joint with J. Goubault-Larrecq). [PDF]

Theses:

  1. Halbgruppen mit Zwischenbedingung
    Staatsexamensarbeit, University of Tübingen (1964). Referees: H. Kneser, K.H. Hofmann.

  2. Beiträge zur Theorie der kompakten abelschen Halbguppen
    Doctoral Dissertation, University of Tübingen (1967).
    Referees: H.H. Schäfer, K.H. Hofmann.
    Published as Articles 2. and 3. above.

  3. Représentations de Groupes et d'Anneaux Réticulés dans des Faisceaux
    Chap. I. Eléments premiers d'un treillis
    Chap. II. L'espace de Stone-Cech-Isbell
    Chap. III. Représentation d'anneaux et de groupes réticulés. Applications.
    [PDF]
    Thèse de Doctorat d'Etat, Faculté des Sciences de Paris (1971).
    Jury: M.-L. Dubreil-Jacotin, J. Dixmier, M.-P. Schützenberger.

Published Seminar Contributions and unpublished Notes:

  1. Topologische Kennzeichnung der geordneten Menge der reellen Zahlen,
    Seminarvortrag, Universität Tübingen, Dez. 1961, 3pp. [PDF]
  2. Demi-groupes compacts solénoidaux et cylindriques (d'après Hofmann-Mostert),
    Séminaire Dubreil--Pisot (Algèbre et Théorie des Nombres). 19e année, 1965/66, no. 19, 10pp. [PDF]
  3. Un Théorème sur les demi-groupes compacts commutatifs,
    Séminaire Dubreil-Pisot (Algèbre et Théorie des Nombres). 23e année, 1969/70, DG4, 4pp. [PDF]
  4. Stone duality for varieties generated by quasi-primal algebras,
    Proc. Conf. Lattice Theory, Houston (1974), pp. 452--454, (joint with H.Werner.)
  5. Conditions de Mal'cev et algèbres universelles uniformes,
    Séminaire Dubreil (Algèbre), 27 année (1973/74), Fasc. 2, Exposé 11, 5pp. [PDF]
  6. Représentation des algèbres universelles par des faisceaux,
    Séminaire Dubreil (Algèbre), 27 année (1973/74), Fasc. 2, Exposé 12, 9pp. [PDF]
  7. Topologische Darstellung von Verbänden,
    Proceedings Lattice Theory Conference, Ulm (1976), pp. 118-133, (joint with G.Gierz.)
  8. Remarks on pointwise infima of lower semicontinuous functions,
    draft [PDF]
  9. Valuations and Measures, (joint with R. Tix), preliminary draft.
  10. Bi-continuous domains and some old problems in domain theory,
    Talk at DOMAINS IX, Brighton 2008. [PDF]
  11. Reasoning about programs combining probability and nondeterminism in a probabilistic logic
    over continuous state spaces     , (joint with Ying Mingsheng). [PDF]
  12. Refinement calculus with probability or fuzziness,
    (joint with Ying Mingsheng and Chen Yixiang). [PDF]
  13. Georg Cantor in Darmstadt. (Documents from the archive of the University of Technology at Darmstadt) [PDF]

Other Publications:

  1. Abstract approximation theory, in: M. Hazewinkel (ed.), Encyclopaedia of Mathematics, Supplement vol. I, Kluwer Academic Publishers  (1997), pp. 11--12 (joint with W. Roth).
  2. Book Review: S. Wolfenstein (ed.), Algebra and Order, Proceedings of the First International Symposium on Ordered Algebraic Structures, Luminy-Marseille 1984, Heldermann-Verlag 1986 Order 5 (1988), pp. 319--321.
  3. Samuel Wolfenstein in memoriam, Order 5 (1988), pp. 105-106.
  4. Ergebnisse der Arbeitsgruppe 4: Mathematik, Tagungsdokumentation Bachelor und Master in Mathematik und Naturwissenscahften, in Dokumentationen und Materialien Bd. 39, DAAD und HRK (2000), pp. 287-293.
  5. Verstetigung internationaler Studiengänge: Vom Pilotprojekt zur Einrichtung auf Dauer. In: Die internationale Hochschule: Studium. Ein Handbuch für Politik und Praxis, Band 2, W. Bertelsmann Verlag (2003), pp. 104-111.
  6. A mathematician's view of an Italian 15th century painting: The Annunciation, with St. Emidius, by Carlo Crivelli (in Japanese). Jinkan Forum, Kyoto University 28 (2011), pp. 54--59 (joint with K. H. Hofmann). [PDF, go to p. 57]