Klaus Keimel



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

  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.) [e-book]

  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.) [e-book]

  6. Semantic Domains for Combining Probability and Non-Determinism
    Electronic Notes in Theoretical Computer Science 129 (2005), 104 pages.
    The numbering system in the above has been screwed up completely,
    so it has been republished with a corrected numbering: 222 (2009), 99 pages (joint with R. Tix and G.D. Plotkin). [PDF]
    Corrigendum for Lemma 4.29[PDF]

Book Chapter

  1. Continuous and Completely Distributive Lattices
    Chapter I (pages 5--53) in: G. Grätzer and F. Wehrung (Eds.)
    Lattice Theory: Special Topics and Applications, Vol. 1, Birkhäuser, 2014 (joint with J. D. Lawson)

Articles in Journals and Refereed Proceedings:

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

  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, Série A, 266 (1968), pp. 124-127.[Electronic Access]

  5. Anneaux réticulés quasiréguliers et hyperarchimédiens
    C.R. Acad. Sc. Paris, Série A, 226 (1968), pp. 524-525. [Electronic Access]

  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, Série A, 267 (1968), pp. 589-591. [Electronic Access]

  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.) [Electronic access]

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

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

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

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

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

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

  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). [Electronic Access]

  20. Stone Dualität für primitive Klassen, die von quasi-primalen Algebren erzeugt werden
    In Hans-J. Hoehnke (ed.): Universelle Algebren und Theorie der Radikale. Akademie--Verlag Berlin  (1976), pp. 23--28 (joint with H. Werner).

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

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

  23. 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).

  24. 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).[Electronic Access]

  25. 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]

  26. 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]

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

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

    Remarks on pointwise infima of lower semicontinuous functions, Notes added after 1984 [PDF]

  29. 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, look for backmatter]

  30. 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.)

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

  32. A direct proof of the Hofmann-Mislove theorem
    Proc. Amer. Math. Soc. 120 (1994), pp. 301-303 (joint with J. Paseka). [Electronic Access ]

  33. 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).

  34. 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.

  35. 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]

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

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

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

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

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

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

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

  43. Topological cones: Foundations for a domain theoretical Semantics combining probability and nondeterminism
    In: M. Escardo, 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]

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

  45. 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]

  46. Topological Cones: Functional analysis in a T0-setting
    Semigroup Forum 77 (2008), pp. 108--142. [PDF]

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

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

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

  50. 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]

  51. 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]

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

  53. 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]

  54. Extending algebraic operations to D-completions
    Electronic Notes in Theoretical Computer Science 249 (2009), 93--116
    Extended version: Theoretical Computer Science 430 (2012),  73--87 (joint with J.D.Lawson). [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]

  56. Locally convex cones and the Schroeder-Simpson Theorem
    Quaestiones Mathematicae 35   (2012), 353--390. [PDF]

  57. On the equivalence of state transformer semantics and predicate transformer semantics
    Proceedings of the Workshop Informatics and Information Technologies in Education: Theory, Practice, Didactics, Novosibirsk, vol. 1   (2012), 78--104. [PDF]

  58. Imprecise probabilities, bets, and functional analytic methods in Lukasiewicz logic
    Forum Mathematicum 25(2)   (2013), 405--441 (joint with M. Fedel, F. Montagna and W. Roth). DOI 10.1515/FORM.2011.123 [PDF]

  59. Quasicontinuous domains and the Smyth powerdomain
    Electronic Notes in Theoretical Computer Science 298   (2013), 215--232 (joint with R. Heckmann) [PDF]

  60. Observationally-induced algebras in Domain Theory
    Logical Methods in Computer Science 10(3:18)   (2014), 1--26 (joint with I. Battenfeld and Th. Streicher). [PDF]

  61. Weakly Compact Spaces of Homomorphisms in Asymmetric Topology
    Topology and its Applications 185-186   (2015), 1--22. [PDF]

  62. Weak upper topologies und duality of cones
    Logical Methods in Computer Science 11(3:21)   (2015), 1--14. [PDF]

  63. Healthiness conditions for predicate transformers
    Electronic Notes in Theoretical Computer Science 319   (2015), 255--270. [PDF]

  64. Mixed Powerdomains for Probability and Nondeterminism
    Logical Methods in Computer Science 13(1:2)   (2017), 1--84. (joint with G. D. Plotkin) [LMCS]

  65. The Cuntz semigroup and domain theory
    Soft Computing 21(10)   (2017), 2485-2502. DOI 10.1007/s00500-017-2573-z [arXiv]

  66. Domain Theory, its Ramifications and Interactions
    Electronic Notes in Theoretical Computer Science (to appear). [ENTCS]


  1. Halbgruppen mit Zwischenbedingung
    (Semigroups with betweenness relations)
    Staatsexamensarbeit, Universität Tübingen (1964). Referees: H. Kneser, K.H. Hofmann.
    [Einleitung, Bibliographie, Kap. I, II], [Kap. III.1, III.2], [Kap. III.3, IV]

  2. Beiträge zur Theorie der kompakten abelschen Halbguppen
    (Contributions to the theory of compact semigroups)
    Doctoral Dissertation, Universität Tübingen (1967).
    Referees: H.H. Schäfer, K.H. Hofmann.
    Published as Articles number 2. and 3. above.

  3. Représentations de Groupes et d'Anneaux Réticulés dans des Faisceaux
    Thèse de Doctorat d'Etat, Faculté des Sciences, Université Paris VI (1971).
    Jury: M.-L. Dubreil-Jacotin (président), J. Dixmier (rapporteur), M.-P. Schützenberger (2e thèse).

    Scanned from the original:
    Frontpages and Introduction [PDF]
    Chapitre I. Eléments premiers d'un treillis [PDF]
    Chapitre II. L'espace de Stone-Cech-Isbell [PDF]
    Chapitre III. Représentation d'anneaux et de groupes réticulés. Applications.
    Bibliographie, Index, Table de Matièeres [PDF]

    Copied from the original: [PDF]

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. Abstract Approximation Theory,
    Encyclopedia of Mathematics, Springer Verlag (joint with W. Roth)[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. Sheaf Representations of algebraic systems. A personal historical account. (August 27, 2013) arXiv:1308.6249 [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]
  7. Besuch bei einem jungen Maler.
    In der Wochenzeitschrift Christ und Welt vom 9. Oktober 1956, Seite 13. [PDF]