## 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