Seminar on Continuity in Semilattices
Seminar on Continuity in Semilattices (SCS) is a series of memos exchanged 1976-1986 by correspondence among mathematicians, Jimmie Lawson, Karl Heinrich Hofmann, Klaus Keimel, Dana Scott, James Harvey Carruth, J. Winston Crawley, Michael William Mislove, Gerhard Gierz, John R. Liukkonen, Alan Day, Charles Edgar Clark, E.L. Evans, James W. Lea, R.L. Wilson, Oswald Wyler, Morike Kamara, Albert R. Stralka, Heiko Bauer, Jaime Niño, Fred Watkins, Lester W. Jones, John R. Isbell, Rudolf-Eberhard Hoffmann, Marcel Erné, Harmut Gatzke, Hans Dobbertin, and John Albert Tiller.
Two monographs are derived in part from SCS:
A Compendium of Continuous Lattices (Springer 1980) by G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott.
Continuous Lattices and Domains (Cambridge University Press 2003) by G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott.
SCS memos are enumerated in these two monographs.
The results in these memos were never refereed. After being refereed and corrected, many of these results were published in the two monographs and other publications.
Errata for Continuous Lattices and Domains are posted below under "Additional unnumbered documents associated with SCS."
Many SCS memos are also accessible at https://www2.mathematik.tu-darmstadt.de/~logik/keimel/scs.html
SCS memos enumerated in the 1980 and 2003 monographs
SCS 1: More Notes on Spread
Jimmie D. Lawson
SCS 2: Notes on Notes by JDL (Concerning What He Calls the 'Spread')
Karl Heinrich Hofmann
SCS 3: Equationally Compact SENDOs are Retracts of Compact Ones
Klaus Keimel and Karl Heinrich Hofmann
SCS 4: Note on Continuous Lattices
Dana S. Scott
SCS 5: Notes on Chains in CL-Objects
Karl Heinrich Hofmann
SCS 6: More Notes on Chains in CL-Objects
James H. Carruth, Charles E. Clark, J. Winston Crawley, E. L. Evans, and R. L. Wilson
SCS 7: Still More Notes on Chains in CL-Objects
James H. Carruth
SCS 8: On the Theorem of Lawson's that all Compact Locally Connected Finite Dimensional Semilattices are CL
Karl Heinrich Hofmann and Michael Mislove
SCS 9: Commentary on Scott's Function Spaces
Karl Heinrich Hofmann and Michael Mislove
SCS 10: Points with Small Semilattices
Jimmie D. Lawson
SCS 11: Errata and Corrigenda to Memo "Commentary on Scott's Function Spaces"
Karl Heinrich Hofmann and Michael Mislove
SCS 12: Relations with the Interpolation Property and Continuous Lattices
Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, and Michael Mislove
SCS 13: Complements to Relations with the Interpolation Properties and Continuous Lattices
Klaus Keimel
SCS 14: SCS Memo of Lawson Dated 7-12-76
Michael Mislove
SCS 15: Continuous Lattices and Universal Algebra
Dana S. Scott
SCS 16: The Random Unit Interval (Another Example of a CL-Object)
Karl Heinrich Hofmann and John R. Liukkonen
SCS 17: The Space of Lower Semicontinuous Functions into a CL-Object, Applications (Part I): Copowers in CL
Karl Heinrich Hofmann
SCS 19: Several Remarks
Klaus Keimel and Michael Mislove
SCS 20: More on the Coproduct. Errata and Addenda
Karl Heinrich Hofmann
SCS 21: ≤ (n)
James H. Carruth, Charles E. Clark, E. L. Evans, James W. Lea, and R. L. Wilson
SCS 22: Representations of Colimits in CL, Part I
Gerhard Gierz
SCS 22: Representations of Colimits in CL, Part II
Gerhard Gierz
SCS 23: Non-Continuous Lattices
Jimmie D. Lawson
SCS 24: An Editorial
Karl Heinrich Hofmann and Klaus Keimel
SCS 25: Observations
Karl Heinrich Hofmann
SCS 26: A Reply to an Editorial
Dana S. Scott
SCS 27: Closure Operators and Kernel Operators in CL
Michael Mislove
SCS 28: The Lattice of Open Subsets of a Topological Space
Klaus Keimel and Michael Mislove
SCS 29: On the Closedness of the Set of Primes in Continuous Lattices
Karl Heinrich Hofmann and Oswald Wyler
SCS 30: Continuous Semilattices and Duality
Jimmie D. Lawson
SCS 31: The Lattice of Ideals of a C*-Algebra
Karl Heinrich Hofmann
SCS 32: The Spectral Theory of Distributive Continuous Lattices
Karl Heinrich Hofmann and Jimmie D. Lawson
SCS 33: Complement to "The Spectral Theory of Distributive Continuous Lattices"
Karl Heinrich Hofmann and Jimmie D. Lawson
SCS 34: On Complete Lattices L for which O(L) is Continuous - A Lattice Theoretical Characterization of CS.
Gerhard Gierz and Karl Heinrich Hofmann
SCS 39: Quotients of Cubes
Albert R. Stralka
SCS 41: An Exercise on the Spectrum of Function Spaces
Karl Heinrich Hofmann and Dana S. Scott
SCS 42: Generalized Continuous Lattices
Gerhard Gierz and Jimmie D. Lawson
SCS 43: Locally Quasicompact Sober Spaces are Baire Spaces
Karl Heinrich Hofmann
SCS 44: Remark on Hofmann's SCS Memo 1/18/78
Klaus Keimel and Heiko Bauer
SCS 46: A Result about O(X)
Gerhard Gierz, Jimmie D. Lawson, and Michael Mislove
SCS 47: Équivalence des espaces de Batdedat et des treillis algébriques
Karl Heinrich Hofmann
SCS 48: Projective Limits in CL and Scott's Construction (Comp. III-3)
Karl Heinrich Hofmann and Jaime Niño
SCS 49: A Review of a Theorem of Dixmier's
Karl Heinrich Hofmann and Fred Watkins
SCS 50: Scott Continuous Closure Operators and Modal Operators. More Self Functors to which the Scott Construction Applies
Karl Heinrich Hofmann and Lester W. Jones
SCS 51: A New Lemma on Primes and a Topological Characterization of the Category DCL of Continuous Heyting Algebras and CL-Morphisms
Karl Heinrich Hofmann and Fred Watkins
SCS 52: Bemerkungen zum "Neuen Lemma"
Karl Heinrich Hofmann and Klaus Keimel
SCS 53: Completely Distributive Algebraic Lattices
Karl Heinrich Hofmann
SCS 54: CL-projective Limits of Distributive Continuous Lattices are Distributive
Karl Heinrich Hofmann
SCS 55: MC Direct Limits
John R. Isbell
SCS 56: On a Question of O. Wyler
Karl Heinrich Hofmann and Klaus Keimel
SCS 57: On the Duality of Semilattices
Karl Heinrich Hofmann and Jimmie D. Lawson
SCS 58: The CL-Compactification of a Continuous Poset
Rudolf-Eberhard Hoffmann
SCS 59: Sober Quotients
John R. Isbell
SCS 60: Miniworkshop on Continuous Lattices at Tulane University from Thursday, November 19, 1981 through Saturday, November 21, 1981
Karl Heinrich Hofmann
SCS 61: The Category CD of Completely Distributive lattices and Their Free Objects
Karl Heinrich Hofmann
SCS 62: Continuous Posets: Injective Hull and MacNeille Completion
Rudolf-Eberhard Hoffmann
SCS 63: The Fell Compactification
Rudolf-Eberhard Hoffmann
SCS 64: A Continuous Poset whose Compactification is not a Continuous Poset. The Square is the Injective Hull of a Discontinuous CL-Compact Poset
Karl Heinrich Hofmann and Michael Mislove
SCS 65: Bernhardina (The Essential Hull Revisited)
Karl Heinrich Hofmann
SCS 66: Revision of [SCS 64]
Karl Heinrich Hofmann and Michael Mislove
SCS 68: A Remark on the Complete Distributivity of Algebraic Lattices
Karl Heinrich Hofmann
SCS 71: Two Remarkable Continuous Posets and an Appendix to "The CL-Compactification and the Injective Hull of a Continuous Poset"
Rudolf-Eberhard Hoffmann
SCS 73: Meet-Continuous Lattices in which Meet is not Continuous
Marcel Erné and Hartmut Gatzke
SCS 74: Distributive Semilattices
Hans Dobbertin
SCS 76: 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
Rudolf-Eberhard Hoffmann
SCS 77: On the Pseudo-Spectrum of a Continuous Distributive Lattice
Karl Heinrich Hofmann
SCS 78: "Duality" for Distributive Compact Multiplicative Continuous Lattices
Rudolf-Eberhard Hoffmann
SCS 81: Intrinsic Topologies on Semilattices of Finite Breadth
Gerhard Gierz, Jimmie D. Lawson, and Albert R. Stralka
SCS 82: Compactifying Distributive Lattices
Gerhard Gierz and Albert R. Stralka
SCS 84: The Zariski Topology on Semilattices and Essential Extensions
Gerhard Gierz and Albert R. Stralka
SCS 85: The Space of Compact Convex Subsets of a Locally Convex Topological Vector Space
Klaus Keimel
SCS 87: The Way-Below Relation is not What I Think
John Albert Tiller
SCS 88: A Proof of a Theorem of B. B.
Klaus Keimel
SCS 93: Refinement Monoids
Hans Dobbertin
Additional unnumbered documents associated with SCS
An Error in the Copower Considerations
Gerhard Gierz and Klaus Keimel
Letter Dated October 13, 1976 to Jimmie D. Lawson
Karl Heinrich Hofmann
Meet-Continuous Lattices in which Meet is not Continuous
Marcel Erné and Hartmut Gatzke
Convexities
Jimmie D. Lawson
Odds and Ends
Jimmie D. Lawson
Errata: Continuous Lattices and Domains
Jimmie D. Lawson