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Projective sober spaces

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Continuous Lattices

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 871))

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References

  1. Alexandrov, P.S.: Diskrete Räume. Mat Sbornik 2, 501–519 (1937).

    MATH  Google Scholar 

  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. Banaschewski, B.: Essential extensions of To-spaces. General Topology Appl. 7, 233–246 (1977).

    MathSciNet  MATH  Google Scholar 

  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. Bruns, G.: Darstellungen und Erweiterungen geordneter Mengen I,II. J.reine angew.Math. 209, 167–200 (1962) and 210, 1–23 (1962).

    MathSciNet  Google Scholar 

  6. Császár, A.: Grundlagen der allgemeinen Topologie. Akad. Kiadó: Budapest 1963.

    MATH  Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  8. Georgescu, G. and B. Lungulescu: Sur les propriétés topologiques des structures ordonnées. Revue Roumaine Math.Pures Appl.14, 1453–1456 (1969).

    MathSciNet  MATH  Google Scholar 

  9. Gleason, A.M.: Projective topological spaces. Illinois J.Math. 2, 482–489 (1958).

    MathSciNet  MATH  Google Scholar 

  10. Hardie, K.A.: Projectivity and injectivity relative to a functor. Math.Colloq., Univ.Cape Town 10, 68–80 (1975/6).

    MathSciNet  Google Scholar 

  11. Herrlich,H.: Topologische Reflexionen und Coreflexionen. Springer LNM 78 (1968).

    Google Scholar 

  12. Hoffmann, R.-E.: Factorization of cones.Math.Nachr. 87, 221–238(1979).

    Article  MathSciNet  MATH  Google Scholar 

  13. —: Charakterisierung nüchterner Räume. Manuscripta math. 15, 185–191 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  14. —: Irreducible filters and sober spaces. Manuscripta math. 22, 365–380 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  15. —: Sobrification of partially ordered sets. Semigroup Forum 17, 123–138 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  16. —: Essentially complete To-spaces. Manuscripta math. 27, 401–432 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  17. —: Continuous posets and adjoint sequences. Semigroup Forum 18, 173–188 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  18. Hofmann, K.H. and J.D. Lawson: The spectral theory of distributive continuous lattices. Trans.Amer.Math.Soc.246, 285–310 (1978/9).

    Article  MathSciNet  MATH  Google Scholar 

  19. Isbell, J.R. Function spaces and adjoints.Math.Scand 36, 317–339 (1975).

    MathSciNet  MATH  Google Scholar 

  20. Kowalsky, H.J.: Verbandstheoretische Kennzeichnung topologischer Räume. Math.Nachr. 21 297–318 (1960).

    Article  MathSciNet  MATH  Google Scholar 

  21. Lawson,J.D.: Continuous semilattices and duality. Memo, Jan.4, 1977 (distributed to members of SCS).

    Google Scholar 

  22. Mac Lane, S.: Categories for the working mathematician. Springer: Berlin-Heidelberg-New York 1971.

    Book  MATH  Google Scholar 

  23. Maranda, J.M.: Injective structures. Trans.Amer.Math.Soc. 110, 98–135 (1964).

    Article  MathSciNet  MATH  Google Scholar 

  24. Markowsky, G.: Chain-complete posets and directed sets with applications. Algebra Universalis 6, 53–68 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  25. —: A motivation and generalization of Scott's notion of a continuous lattice. Preprint. Revised version: These Proceedings.

    Google Scholar 

  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).

    Article  MathSciNet  MATH  Google Scholar 

  27. Plotkin, G.D.: A powerdomain construction. SIAM J.Computing 5, 452–487 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  28. Schubert, H.: Categories. Springer: Berlin-Heidelberg-New York, 1972.

    Book  MATH  Google Scholar 

  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. —: Continuous lattices. In: Proc. Dalhousie conf. on toposes, algebraic geometry and logic, pp.97–136. Springer LNM 274(1972).

    Google Scholar 

  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. Semadeni, Z.: Banach spaces of continuous functions. PWN (Polish Scientific Publishers): Warszawa 1971.

    MATH  Google Scholar 

  33. Ward, A.J.: Representations of proximity lattices. Ann.Univ. Sci.Budapest Rolando Eötvös, Sect.Math.17,41–57 (1975).

    MathSciNet  MATH  Google Scholar 

  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. Wyler,O.: Dedekind complete posets and Scott topologies. Memo, April 18,1977 (distributed to members of SCS). Revised version: These Proceedings.

    Google Scholar 

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Authors and Affiliations

  1. Fachbereich Mathematik, Universität Bremen, D-28, Bremen, Federal Republic of Germany

    Rudolf-E. Hoffmann

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  1. Rudolf-E. Hoffmann
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Bernhard Banaschewski Rudolf-Eberhard Hoffmann

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© 1981 Springer-Verlag

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Hoffmann, RE. (1981). Projective sober spaces. In: Banaschewski, B., Hoffmann, RE. (eds) Continuous Lattices. Lecture Notes in Mathematics, vol 871. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089906

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  • DOI: https://doi.org/10.1007/BFb0089906

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10848-1

  • Online ISBN: 978-3-540-38755-8

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