SCS --- Seminar on Continuity in Semilattices
1976 -- 1984

Informal Seminar by correspondence around Continuous Lattices.

The material in these notes during the first years often was not published in papers but entered directly in the monograph:
A Compendium of Continuous Lattices.
G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove, D. S. Scott
Springer Verlag, 1980.

    Editorial 1979
    List of Participants 1983
    Some Errata in the Compendium of Continuous Lattices

    1. 19 Jan 1976 Lawson, J. D.,
      More notes on spreads.
    2. 19 Jan 1976 Hofmann, K. H.,
      Notes on Memo [SCS-1]..
    3. 29 Jan 1976 Keimel, K.,
      Equationally compact SEND0s are retracts of compact ones.
    4. 30 Mar 1976 Scott, D. S.,
      Note on continuous lattices.
    5. 19 Apr 1976 Hofmann, K. H.,
      Notes on chains in CL-objects.
    6. 28 May 1976 Carruth, J. H., et al.,
      More notes on chains in CL-objects.
    7. 15 Jun 1976 Carruth, J. H., et al.,
      Still more notes on chains in CL-objects.
    8. 28 Jun 1976 Hofmann, K. H. and Mislove, M. W.,
      On the theorem of Lawson's that all compact locally connected finite dimensional semilattices are CL.
    9. 07 Jul 1976 Hofmann, K. H. and Mislove, M. W.,
      Commentary on Scott's function spaces.
    10. 12 Jul 1976 Lawson, J. D.,
      Points with small semilattices.
    11. 20 Jul 1976 Hofmann, K. H. and Mislove, M. W.,
      Errata and corrigenda to Memo [SCS-9].
    12. 01 Aug 1976 Gierz, G., Hofmann, K. H., Keimel, K., and Mislove, M. W.,
      Relations with the interpolation property and continuous lattices. First Part.
      Second part.
    13. 10 Aug 1976 Keimel, K.,
      Complements to relations with the interpolation property and continuous lattices.
    14. 18 Aug 1976 Mislove, M. W.,
      On Memo [SCS-10].

    15. 23 Aug 1976 Scott, D. S.,
      Continuous lattices and universal algebra.
    16. 01 Sep 1976 Hofmann, K. H. and Liukkonen, J. R.,
      The random unit interval (another example of a CL-object).
    17. 20 Sep 1976 Hofmann, K. H.,
      The space of lower semicontinuoue functions into a CL-object, Applications (Part I): Copowers in CL.
    18. 21 Sep 1976 Day, A.,
      Continuous lattices and universal algebra.
    19. 30 Sep 1976 Keimel, K. and Mislove, M. W.,
      Several remarks:
      1. The closed subsemilattices of a continuous lattice form a continuous lattice.
      2. When do the prime elements of a distributive lattice form a closed subset.
      3. On lower semicontintuous function spaces.
      4. On the continuity of the congruence lattice of a continuous lattice.
    20. 23 Oct 1976 Hofmann, K. H.
      More on the coproduct. Errata and addenda.
    21. 10 Nov 1976 Carruth, J. H., Clark, C. E., Evans, E., Lea, J. W., Jr. and Wilson, R. L.
    22. 10 Nov 1976 Gierz, G.
      Representation of colimits in CL. Part I. Part_II.
    23. 19 Nov 1976 Lawson, J. D.
      Non-continuous lattices.
    24. 19 Nov 1976 Hofmann, K. H. and Keimel, K.
    25. 23 Nov 1976 Hofmann, K. H.
    26. 30 Nov 1976 Scott, D. S.
      A reply to an editorial.
    27. 08 Dec 1976 Mislove, M. W.
      Closure operators and kernel operators in CL.
    28. 15 Dec 1976 Keimel, K. and Mislove, M. W.
      The lattice of open subsets of a topological space.
    29. 28 Dec 1976 Hofmann, K. H. and Wyler, 0.
      On the closedness of the set of primes in a continuous lattice.
    30. 04 Jan 1977 Lawson, J. D.
      Continuous semilattices and duality.
    31. 13 Jan 1977 Hofmann, K. H.
      The lattice of ideals of a C∗-algebra.
    32. 08 Feb 1977 Hofmann, K. H. and Lawson, J. D.
      The spectral theory of continuous lattices.
    33. 14 Mar 1977 Hofmann, K. H. and Lawson, J. D.
      Complement to Memo [SCS-32].
    34. 08 Apr 1977 Gierz, G. and Hofmann, K. H.
      On complete lattices for which O(L) is continuous - a lattice theoretical characterization of CS.
    35. 18 Apr 1977 Wyler, 0.
      Dedekind complete posets and Scott topologies.
    36. 16 May 1977 Scott, D. S.
      Quotients of distributive continuous lattices: a result of S.A. Jalali.
    37. 20 May 1977 Wyler, 0.
      Comments on the spectral theory of continuous lattices.
    38. 01 Jul 1977 Kamara, M.
      Treillis continus et treilis completement distributifs.
    39. 15 Jul 1977 Stralka, A. R.
      Quotients of cubes.
    40. 28 Jul 1977 Mislove, M. W.
      A new approach to some results of Lawson, Gierz and Hofmann.
    41. 25 Sep 1977 Hofmann, K. H. and Scott, D. S.
      An exercise on the spectrum of function spaces.
    42. 02 Nov 1977 Gierz, G. and Lawson, J. D.
      Generalized continuous lattices .
    43. 18 Jan 1978 Hofmann, K. H.
      Locally quasicompact sober spaces are Baire spaces.
    44. 09 Feb 1978 Bauer, H. and Keimel, K
      Remark on the Memo [SCS-43].
    45. 15 Apr 1978 Bauer, H.
      Antichains and equational compactness.
    46. 19 May 1978 Gierz, G., Lawson, J. D. and Mislove, M. W., A result about O(X).
    47. 28 May 1978 Hofmann, K. H.
      Equivalence des espaces de Batbedat et des treillis algebriques.
    48. 29 Nov 1978 Hofmann, K. H. and Nino, J.
      Projective limits in CL and Scott’s construction.
    49. 30 Nov 1978 Hofmann, K. H. and Watkins, F.
      A review of a theorem of Dixmier’s.
    50. 30 May 1979 Hofmann, K. H. and Jones, L. W., Jr..
      Scott continuous closure operators and modal operators. More self functors to which the Scott construction applies.
    51. 30 May 1979 Hofmann, K. H. and Watkins, F..
      A new Lemma on primes and a topological characterization of the eategory DCL of continuous Heyting algebras and CL-morphisms.
    52. 11 Jun 1979 Hofmann, K. H. and Keimel, K..
      Bemerkungen zum ”Neuen Lemma”.
    53. 27 Nov 1979 Hofmann, K. H., Completely distributive algebraic lattices.
    54. 29 Feb 1980 Hofmann, K. H..
      CL-projective limits of distributive continuous lattices are distributive.
    55. 19 Mar 1980 Isbell, J. R..
      MC direct limits.
    56. 26 Oct 1980 Hofmann, K. H. and Keimel, K.
      On a question of O. Wyler.
    57. 19 Nov 1980 Hofmann, K. H. and Lawson, J. D..
      On the duality of semilattices.
    58. 10 Sep 1981 Hoffmann, R.-E..
      The CL-compactification of a continuous poset. Abstract.
    59. 22 Nov 1981 Isbell, J. R.
      Sober quotients.
    60. 23 Nov 198 Hofmann, K. H.
      Miniworkshop on Continuous Lattices at Tulane University, Nov 19-21, 1981.
    61. 24 Nov 1981 Hofmann, K. H.
      The category CD of completely distributive lattices and their free objects.
    62. 01 Dec 1981 Hoffmann, R.-E.
      Continuous posets: Injective hull and MacNeille completion.
    63. 11 Mar 1982 Hoffmann, R.-E.
      The Fell compactification. Abstract.
    64. 28 May 1982 Hofmann, K. H. and Mislove, M. W.
      A continuous poset whose compactification is not a continuous poset. The square is the injective hull of a discontinuous CL-compact poset.
    65. 08 Jun 1982 Hofmann, K. H.
      Bernhardina - the essential hull revisited.
    66. 02 Jul 1982 Hofmann, K. H. and Mislove, M. W.
      Revision of [SCS-64].
    67. 05 Jul 1982 Lawson, J. D.
      A strict extension of previous results on essential extensions.
    68. 16 Jul 1982 Hofmann, K. H.
      A remark on the complete distributivity of algebraiclattices.
    69. 23 Jul 1982 Erne, M.
      Order generation and distributive laws in complete lattices.
    70. 25 Jul 1982 Erne, M.
      Freedom for completely distributive lattices (over continuous posets).
    71. 28 Jul 1982 Hoffmann, R.-E.
      Two remarkable continuous posets and an appendix to ’The CL-compactification and the injective hull of a continuous poset’.
    72. 01 Aug 1982 Erne, M.
      Algebraic posets and compactly generated posets.
    73. 14 Sep 1982 Erne, M. and Gatzke, H.
      Meet-continuous lattices in which meet is not continuous.
    74. 12 Nov 1982 Dobbertin, H.
      Distributive semilattices.
    75. 18 Nov 1982 Dobbertin, H.
      Distributive semilattices, Heyting algebras, and V-homomorphisms.
    76. 09 Jan 1983 Hoffmann, R.-E.
      The trace of the weak topology and of the Γ-topology of L(op) coincide on the pseudo-meet-prime elements of a continuous lattice L.
    77. 12 Jan 1983 Hofmann, K. H.
      On the pseudo-spectrum of a continuous distributive lattice.
    78. 14 Feb 1983 Hoffmann, R. -E.
      ’Duality’ for distributive compact multiplicative continuous lattices.
    79. 14 Jul 1983 Wyler, 0.
      The lower topology for continuous lattices is a monadic functor.
    80. 01 Sep 1983 Wyler, 0.
      Compact ordered spaces and prime Wallman compactifications: summary of results.
    81. 23 Nov 1983 Gierz, G., Lawson, J. D., and Stralka, A. R.
      Intrinsic topologies on semilattices of finite breadth.
      See: Semigroup Forum vol. 31 (1985), 1--17.
    82. 01 Dec 1983 Gierz, G. and Stralka, A. R.
      Compactifying distributive lattices.
    83. 05 Dec 1983 Keimel, K.
      Continuous lattices, general convexity spaces, and a fixed-point theorem.
    84. 06 Dec 1983 Gierz, G. and Stralka, A. R.
      The Zariski topology on semilattices and essential extensions.
    85. 19 Jan 1984 Keimel, K.
      The space of compact convex subsets of a locally convex topological vector space.
    86. Feb 1984 Keimel, K.
      Korovkin theorems for multivalued functions.
    87. 23 Feb 1984 Tiller, J.
      The way-below relation is not what I think.
    88. 01 Apr 1984 Keimel, K.
      A proof of a theorem of BB.
    89. 01 May 1984 Erne, M.
      Continuity concepts for partially ordered sets.
    90. 02 May 1984 Dobbertin, H.
      About polytopes of valuations on finite distributive lattices.
    91. 07 May 1984 Erne, M.
      Compactly generated and continuous closure systems.
    92. 14 May 1984 Erne, M.
      Products of Continuous partially ordered sets.
    93. 15 May 1984 Dobbertin, H.
      Refinement monoids.
    94. 03 Jul 1984 Wyler, O.
      Algebraic theories for proper filter monads.
      10 Feb 1985 Dobbertin, H.
      A remark on congruence lattices of lattices.
    95. 10 Mar 1985 Erne, M.
      Fixed point constructions for standard completions.
    96. 18 Mar 1985 Erne, M.
      Generators and weights of completely distributive lattices.
    97. 05 Oct 1985 Erne, M.
      , Z-continuous posets, Z-ary closure spaces and generalized soberness.
    98. 04 Jun 1986 Erne, M.
      Z-continuity, Z-hypercompactness and complete distributivity.