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Sobrification of partially ordered sets

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References

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

    Google Scholar 

  2. Andima, Susan J. and W.J. Thron:Order-induced topological properties. Trans.Amer.Math.Soc. (to appear).

  3. Artin,M., A.Grothendieck, and J. Verdier: Théorie des topos et cohomologie étale des schémas. Lect.Notes in Math. 269 (1972) (rev.ed. of SGA 4, 1962/1963).

  4. Aull,C.E. and W.J.Thron:Separation axioms between T0 and T1. Indag.Math.24 (1963), 26–37.

    Google Scholar 

  5. Banaschewski,B.:Essential extensions of T0-spaces. Gen. Topology Appl. 7 (1977), 233–246.

    Google Scholar 

  6. Bourbaki,N.:Algébre commutative (chap.2:Localisation) Paris: Hermann 1961.

    Google Scholar 

  7. Bruns,G.:Darstellungen und Erweiterungen geordneter Mengen I und II. J.f.d.reine u.angewandte Math. 209 (1962), 167–200, respectively, 210(1962), 1–23.

    Google Scholar 

  8. Day,B.J. and G.M.Kelly:On topological quotient maps preserved by pullbacks or products. Proc.Cambridge Philos. Soc.67 (1970), 553–558.

    Google Scholar 

  9. Frink,O.:Ideals in partially ordered sets. Amer.Math. Monthly 61 (1954), 223–234.

    Google Scholar 

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

    Google Scholar 

  11. Grätzer,G.:Universal Algebra. Van Nostrand: Princeton N.J. 1968.

    Google Scholar 

  12. Herrlich,H.:Topologische Reflexionen und Coreflexionen. Lect.Notes in Math. 78(1968).

  13. Hochster,M.:Prime ideal structure in commutative rings. Trans.Amer.Math.Soc. 142 (1969), 43–60.

    Google Scholar 

  14. Hoffmann,R.-E.:Charakterisierung nüchterner Räume. Manuscripta Math. 15 (1975), 185–191.

    Google Scholar 

  15. —:Topological functors admitting generalized Cauchy-completions. In: Categorical Topology. Proc. of the Conf. held at Mannheim 1975, pp.286–344. Lect.Notes in Math. 540(1976).

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

    Google Scholar 

  17. Hoffmann,R.-E.:A characterization of a class of categories of topological spaces. Archiv d.Math.30 (1978), 304–316.

    Google Scholar 

  18. —:On the sobrification remainder sX-X.

  19. Hofmann,K.H. and K.Keimel:A general character theory for partially ordered sets and lattices. Memoir Amer.Math. Soc. 122 (1972).

  20. —— and J.D.Lawson:Irreducibility and Generation in Continuous Lattices. Semigroup Forum 13 (1977),307–353.

    Google Scholar 

  21. — and A.R.Stralka:The algebraic theory of compact Lawson semilattices. Dissertationes Math. 137 (1976).

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

    Google Scholar 

  23. Kuratowski,K.:Topology I.Academic Press: New York-London 1966.

    Google Scholar 

  24. Lawson,J.:Continuous semilattices and duality, Memo (Jan.4,1977) Seminar on continuity in semilattices.

  25. Lea, J.W.:Continuous lattices and compact Lawson semi-lattices. Semigroup Forum 13 (1977),387–388.

    Google Scholar 

  26. Rainwater,J.: A note on projective resolutions. Proc. Amer.Math. Soc. 10 (1959), 734–735.

    Google Scholar 

  27. Scott,D.: Continuous lattices. In: Lect.Notes in Math. 274 (1972), 97–136.

    Google Scholar 

  28. Skula,L.:On a reflective subcategory of the category of all topological spaces. Trans.Amer.Math.Soc. 142 (1969), 37–41.

    Google Scholar 

  29. Wyler,O.:Dedekind complete posets and Scott topologies. Memo (April 18, 1977) Seminar on continuity in semilattices.

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Communicated by Karl H. Hofmann

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Hoffmann, RE. Sobrification of partially ordered sets. Semigroup Forum 17, 123–138 (1979). https://doi.org/10.1007/BF02194315

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