Projective sober spaces

  • Rudolf-E. Hoffmann
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 871)


Continuous Lattice Left Adjoint Forgetful Functor Injective Hull Adjoint Functor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alexandrov, P.S.: Diskrete Räume. Mat Sbornik 2, 501–519 (1937).zbMATHGoogle Scholar
  2. 2.
    Artin,M., Grothendieck,A., and J.Verdier: Théorie des topos et cohomologie étale des schémas (SGA IV). Revised edition: Springer LNM 269 (1972).Google Scholar
  3. 3.
    Banaschewski, B.: Essential extensions of To-spaces. General Topology Appl. 7, 233–246 (1977).MathSciNetzbMATHGoogle Scholar
  4. 4.
    —: Projective covers in categories of topological spaces and topological algebras. Proc.Kanpur Topology Conference, 1968, pp. 63–91. Academia: Prague 1971.Google Scholar
  5. 5.
    Bruns, G.: Darstellungen und Erweiterungen geordneter Mengen I,II. J.reine angew.Math. 209, 167–200 (1962) and 210, 1–23 (1962).MathSciNetGoogle Scholar
  6. 6.
    Császár, A.: Grundlagen der allgemeinen Topologie. Akad. Kiadó: Budapest 1963.zbMATHGoogle Scholar
  7. 7.
    Day, B.J. and G.M. Kelly: On topological quotient maps preserved by pullbacks or products. Proc.Cambridge Philos. Soc.67, 553–558 (1970).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Georgescu, G. and B. Lungulescu: Sur les propriétés topologiques des structures ordonnées. Revue Roumaine Math.Pures Appl.14, 1453–1456 (1969).MathSciNetzbMATHGoogle Scholar
  9. 9.
    Gleason, A.M.: Projective topological spaces. Illinois J.Math. 2, 482–489 (1958).MathSciNetzbMATHGoogle Scholar
  10. 10.
    Hardie, K.A.: Projectivity and injectivity relative to a functor. Math.Colloq., Univ.Cape Town 10, 68–80 (1975/6).MathSciNetGoogle Scholar
  11. 11.
    Herrlich,H.: Topologische Reflexionen und Coreflexionen. Springer LNM 78 (1968).Google Scholar
  12. 12.
    Hoffmann, R.-E.: Factorization of cones.Math.Nachr. 87, 221–238(1979).MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    —: Charakterisierung nüchterner Räume. Manuscripta math. 15, 185–191 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    —: Irreducible filters and sober spaces. Manuscripta math. 22, 365–380 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    —: Sobrification of partially ordered sets. Semigroup Forum 17, 123–138 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    —: Essentially complete To-spaces. Manuscripta math. 27, 401–432 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    —: Continuous posets and adjoint sequences. Semigroup Forum 18, 173–188 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Hofmann, K.H. and J.D. Lawson: The spectral theory of distributive continuous lattices. Trans.Amer.Math.Soc.246, 285–310 (1978/9).MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Isbell, J.R. Function spaces and adjoints.Math.Scand 36, 317–339 (1975).MathSciNetzbMATHGoogle Scholar
  20. 20.
    Kowalsky, H.J.: Verbandstheoretische Kennzeichnung topologischer Räume. Math.Nachr. 21 297–318 (1960).MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Lawson,J.D.: Continuous semilattices and duality. Memo, Jan.4, 1977 (distributed to members of SCS).Google Scholar
  22. 22.
    Mac Lane, S.: Categories for the working mathematician. Springer: Berlin-Heidelberg-New York 1971.CrossRefzbMATHGoogle Scholar
  23. 23.
    Maranda, J.M.: Injective structures. Trans.Amer.Math.Soc. 110, 98–135 (1964).MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Markowsky, G.: Chain-complete posets and directed sets with applications. Algebra Universalis 6, 53–68 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    —: A motivation and generalization of Scott's notion of a continuous lattice. Preprint. Revised version: These Proceedings.Google Scholar
  26. 26.
    Markowsky, G. and B.K. Rosen: Bases for chain complete posets. IBM J.Res.Develop.20, 137–147 (1976). Zbl.f.Math.329.06001 (1977).MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Plotkin, G.D.: A powerdomain construction. SIAM J.Computing 5, 452–487 (1976).MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Schubert, H.: Categories. Springer: Berlin-Heidelberg-New York, 1972.CrossRefzbMATHGoogle Scholar
  29. 29.
    Scott,D.: Outline of a mathematical theory of computation. Proc.4th Ann.Princeton Conf. on Inform.Sci. and Systems, pp.169–176 (1970).Google Scholar
  30. 30.
    —: Continuous lattices. In: Proc. Dalhousie conf. on toposes, algebraic geometry and logic, pp.97–136. Springer LNM 274(1972).Google Scholar
  31. 31.
    SCS (=Seminar on Continuity in (Semi-)Lattices): A compendium of continuous lattices, part I: The lattice-theoretical and topological foundations of continuous lattices. Prepared by K.H.Hofmann (chap.I–III), J.Lawson (chap.IV) G.Gierz (chap.V), K.Keimel. Preliminary version (distributed at the workshop II "continuous lattices" at TH Darmstadt, July 1978).Google Scholar
  32. 32.
    Semadeni, Z.: Banach spaces of continuous functions. PWN (Polish Scientific Publishers): Warszawa 1971.zbMATHGoogle Scholar
  33. 33.
    Ward, A.J.: Representations of proximity lattices. Ann.Univ. Sci.Budapest Rolando Eötvös, Sect.Math.17,41–57 (1975).MathSciNetzbMATHGoogle Scholar
  34. 34.
    Wilson, R.L.: Relationships between continuous posets and compact Lawson posets. Abstract 750-A 19, Notices Amer.Math.Soc. 24, A-628 (1977).Google Scholar
  35. 35.
    Wyler,O.: Dedekind complete posets and Scott topologies. Memo, April 18,1977 (distributed to members of SCS). Revised version: These Proceedings.Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Rudolf-E. Hoffmann
    • 1
  1. 1.Fachbereich MathematikUniversität BremenBremenFederal Republic of Germany

Personalised recommendations