Pacific Journal of Mathematics

On the sobrification remainder $^{s}X-X$.

Rudolf-E. Hoffmann

Article information

Source
Pacific J. Math., Volume 83, Number 1 (1979), 145-156.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102784665

Mathematical Reviews number (MathSciNet)
MR555043

Zentralblatt MATH identifier
0421.54018

Subjects
Primary: 54D40: Remainders

Citation

Hoffmann, Rudolf-E. On the sobrification remainder $^{s}X-X$. Pacific J. Math. 83 (1979), no. 1, 145--156. https://projecteuclid.org/euclid.pjm/1102784665


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References

  • [1] P. S. Alexandrov, Diskrete Rdume, Math. Sb., 2 (1937), 501-519.
  • [2] Susan J. Andima and W. J. Thron, Order-induced topological properties, Pacific J. Math., 75 (1978), 297-318.
  • [3] M. Artin, A. Grothendieck and J. Verdier. Theorie des topos et cohomologie etale des schemas, Lect. Notes in Math., 269, Berlin-Heidelberg-New York: Springer 1972 (rev. ed. of SGA 4, 1962/63).
  • [4] C. E. Aull and W. J. Thron, Separation axioms between To and Tlt Indag. Math., 24 (1963), 26-37.
  • [5] N. Bourbaki, Algebre Commutative (Chap. 2: Localisation), Paris: Hermann 1961.
  • [6] N. Bourbaki, General Topology (engl. transl.), Paris: Hermann 1966.
  • [7] G. C. L. Brmmer, Initial quasi-uniformities,Indag. Math., 31 (1969), 403-409.
  • [8] G. Bruns, Darstellungen und Erweiterungengeordneter Mengen I., II., J. reine angew. Math., 209 (1962), 167-200 and, resp. 210(1962), 1-23 (Habilitationsschrift Mainz 1960).
  • [9] J. R. Bchi, Representationsof complete lattices by sets, Portugaliae Math., 11 (1952), 151-167.
  • [10] J. Dieudonne and A. Grothendieck, Elementsde geometrie algebrique, Berlin: Springer 1971.
  • [11] C. H. Dowker and D. Papert, Quotient frames and subspaces, Proc. London Math. Soc, (3) 16 (1966), 275-296.
  • [12] D. Drake and W. J. Thron, On the representationsof an abstract lattice as the familyof closed sets of a topological space, Trans. Amer. Math. Soc, 120 (1965), 57-71.
  • [13] L. Gillman and M. Jerison, Rings of Continuous Functions, New York, Heidelberg: Springer 1976 (2nd print).
  • [14] L. M. Gluskin, B. M. Schein, L. B. Sneperman and J. S. Yaroker, Addendum to a survey of semigroups of continuous self-maps, Semigroup Forum, 14 (1977), 95-125.
  • [15] R. Hartshorne, Algebraic Geometry, New York--Heidelberg--Berlin: Springer 1977.
  • [16] H. Herrlich, Topologische Reflexionen und Coreflexionen, Springer Lecture Notes in Math., 78 (1968).
  • [17] M. Hochster, Prime ideal structure in commutativerings, Trans. Amer. Math. Soc, 142 (1969), 43-60.
  • [18] R.-E. Hoffmann, BemerkungenuberTD-R'ume, Manuscripta Math., 12 (1974), 195-196.
  • [19] R.-E. Hoffmann,CharakterisierungnuchternerR'ume, Manuscripta Math., 15 (1975), 185-191.
  • [20] R.-E. Hoffmann, Topological functors admitting generalized Cauchy-completions, in Cate-
  • [21] R.-E. Hoffmann, Irreducible filters and sober spaces, Manuscripta Math., 22 (1977), 365- 380.
  • [22] S. S. Hong, Extensive subcategories of the category of TQ-spaces,Canad. J. Math., 27 (1975), 311-318.
  • [23] J. R. Isbell, Function spaces and adjoints,Math. Scand., 36 (1975), 317-339.
  • [24] H. J. Kowalsky, Verbandstheoretische. Kennzeichnungtopologischer Rume, Math. Nachr., 21 (1960), 297-318.
  • [25] C. C. Moore and J. Rosenberg, Groups with Tprimitive ideal spaces, J. Functional Analysis, 22 (1976), 204-224.
  • [26] L. D. Nel. Lattices of lower semi-continuousfunctionsand associated topological spaces, Pacific J. Math., 40 (1972), 667-673.
  • [27] L. D. Nel and R. G. Wilson, Epireflectionsin the category of T0-spaces, Fund. Math., 75 (1972), 69-74.
  • [28] L. Skula, On a reflective subcategory of the category of all topological spaces, Trans. Amer. Math. Soc, 142 (1969), 37-41.
  • [29] A. H. Stone, Hereditarilycompact spaces, Amer. J. Math., 82 (1960), 900-916.
  • [30] W. J. Thron, Lattice-equivalence of topological spaces, Duke Math. J., 29 (1962), 671-679. Reseived March 13, 1978 and in revised form November 29, 1978.