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Categorical methods in dimension theory

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Categorical Topology

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Bibliography

  • Aleksandroff, P.S.: On some basic directions in general topology, Russian Math. Surveys 19 (1964), 6.1–39.

    Google Scholar 

  • -: corrections to above, ibid 20 (1965) 1.177–178.

    Google Scholar 

  • Banaschewski, B.: Projective covers in categories of topological spaces and topological algebras, Proc. Kanpur Top. Conference (1968), Academia, Prague, 63–91.

    Google Scholar 

  • Barr, M., Beck, J.: Homology and standard constructions, Lecture Notes in Mathematics 80, Springer-Verlag (1969), 245–335.

    Article  MathSciNet  MATH  Google Scholar 

  • Bartik, V.: Aleksandrov-Čech cohomology and mappings into Eilenberg-MacLane polyhedra, Math. USSR Sbornik 5 (1968), 221–228.

    Article  MATH  Google Scholar 

  • Benabou, J.: Introduction to bicategories, Lecture Notes in Mathematics, 47, Springer-Verlag (1967), 1–77.

    Article  MathSciNet  Google Scholar 

  • Blaszczyk, A.: A factorisation theorem and its application to extremally disconnected resolutions. Colloq. Math. 28 (1974), 33–40.

    MATH  Google Scholar 

  • -: Extremally disconnected resolutions of T 0 -spaces, ibid 32 (1974a), 57–68.

    MathSciNet  MATH  Google Scholar 

  • Bokshtein, M.F.: A new proof of the fundamental theorem of homological dimension theory, Moskov. Gos. Univ. Uch. Zap., 181 Mat. 8 (1956) 13–44.

    Google Scholar 

  • -: The homological theory of dimension, Russian Math. Surveys 21 (1966), 7–12.

    Article  Google Scholar 

  • Bredon, G.E.: Sheaf theory, McGraw-Hill, New York (1967).

    MATH  Google Scholar 

  • Collins, P.J.: Concordant mappings and the concordant-dissonant factorisation of an arbitrary continuous function, Proc. Amer. Math. Soc. 27 (1971), 587–591.

    Article  MathSciNet  MATH  Google Scholar 

  • -: Connection properties in topological spaces, Mathematika Balkancia, 1, (1971a) 44–51.

    MathSciNet  MATH  Google Scholar 

  • Diers, Y.: Complétion monadique, C.R. Acad. Sci. Paris 276 (1973) A1397–A1400.

    MathSciNet  MATH  Google Scholar 

  • Duskin, J.: Simplicial methods and the interpretation of “triple” cohomology, Mem. Amer. Math. Soc. 163 (1975).

    Google Scholar 

  • Dyckhoff, R.: Factorisation theorems and projective spaces in topology Math. Zeitschrift 127 (1972), 256–264.

    Article  MathSciNet  MATH  Google Scholar 

  • -: Perfect light maps as inverse limits, Quart. J. Math. Oxford (2), 25 (1974), 441–449.

    Article  MathSciNet  MATH  Google Scholar 

  • Dyckhoff, R.: Topics in general topology: bicategories, projective covers, perfect mappings and resolutions of sheaves, thesis, Oxford (1974a).

    Google Scholar 

  • -: Projective resolutions of topological spaces J. Pure and Applied Algebra 7 (1976), 115–119.

    Article  MathSciNet  MATH  Google Scholar 

  • Dyckhoff, R.: Categorical Cuts, to appear (1976a).

    Google Scholar 

  • Eilenberg, S.: Sur les transformations continues d'espaces metriques compacts, Fund. Math. 22 (1934), 292–296.

    MATH  Google Scholar 

  • Filippov, V.: On the dimension of closed mappings, Sov. Math. Dokl. 13 (1972), 895–900.

    MATH  Google Scholar 

  • Fourman, M.P.: Comparaison des réelles d'un topos: structures lisses sur un topos élémentaire Amines 1975, to appear in Cah. Top. Geom. Diff.

    Google Scholar 

  • Fourman, M.P.: The logic of topoi, Handbook of mathematical logic (ed. Barwise), North Holland (1976).

    Google Scholar 

  • Freyd, P.: Aspects of topoi, Bull. Austral. Math. Soc., 7 (1972), 1–76.

    Article  MathSciNet  MATH  Google Scholar 

  • Gillman, L., Jerison, M.: Rings of continuous functions, Van Nostrand, Princeton (1960).

    Book  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Godement, R.: Théorie des faisceaux, Hermann Paris (1964).

    MATH  Google Scholar 

  • Gonshor, H.: Projective covers as subquotients of enlargements, Israel J. of Math. 14 (1973), 257–261.

    Article  MathSciNet  MATH  Google Scholar 

  • Goto, T.: Homotopical cohomology groups of paracompact spaces, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 9 (1967), 21–27.

    MathSciNet  MATH  Google Scholar 

  • Gray, J.W.: Formal Category Theory II, Springer Lecture Notes, to appear (1975?).

    Google Scholar 

  • Grothendieck, A., et al.: Théorie des topos et cohomologie etale des schemas, (SGA4), Lecture notes in mathematics 269, Springer-Verlag (1972).

    Google Scholar 

  • Grothendieck, A., et al.: ibid. Théorie des topos et cohomologie etale des schemas, (SGA4), Lecture notes in mathematics 270 (1972a).

    Google Scholar 

  • Hager, A.W.: The projective resolution of a compact space, Proc. Amen. Math. Soc. 28 (1971) 262–266.

    Article  MathSciNet  MATH  Google Scholar 

  • Harris, D.: Katetov extension as a functor, Math. Ann. 193 (1971), 171–175.

    Article  MathSciNet  MATH  Google Scholar 

  • Henriksen, M., Isbell, J.R.: Some properties of compactifications, Duke Math. J. 25 (1958), 83–105.

    Article  MathSciNet  MATH  Google Scholar 

  • Henriksen, M., Jerison, M.: Minimal projective extensions of compact spaces, Duke Math. J. 32, (1965), 291–295.

    Article  MathSciNet  MATH  Google Scholar 

  • Herrlich, H.: Topologische Reflexionen und Coreflexionen Lecture notes in Mathematics, 78, Springer-Verlag, Heidelberg (1968).

    MATH  Google Scholar 

  • -: Categorical topology, General topology and its applications 1, (1971) 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  • Herrlich, H.: A generalisation of perfect maps, Proc. Third Prague Top. Symposium 1971, Academia Prague (1973) 187–192.

    Google Scholar 

  • -: Perfect subcategories and factorisations Proc. Hungarian Top. Conference 1972=Topics in topology, (ed. A. Czaszar), Coll. Math. Soc. Janos Bolyai, 8, North-Holland, Amsterdam (1974).

    Google Scholar 

  • Huber, P.J.: Homotopical cohomology and Čech cohomology, Math. Ann. 144 (1961), 73–76.

    Article  MathSciNet  MATH  Google Scholar 

  • Hurewicz and Wallman, Dimension theory, Princeton (1948).

    Google Scholar 

  • Isbell, J.R.: Subobjects, adequacy, completeness, and categories of algebras, Rozprawy Mat. 38, (1963) 1–32.

    Google Scholar 

  • Johnstone, P.: Aspects of internal category theory, thesis, Cambridge (1974).

    Google Scholar 

  • Kennison, J.F.: Full reflective subcategories and generalised covering spaces, Illinois J. Math. 12, (1968) 353–365.

    MathSciNet  MATH  Google Scholar 

  • Kock, A., Wraith, G.C.: Elementary topoi, Aarhus lecture notes, 30 (1971).

    Google Scholar 

  • Kulpa, W.: Factorisation and inverse expansion theorems for uniformities, Colloq. Math. 21, (1970) 217–227.

    MathSciNet  MATH  Google Scholar 

  • Kuz'minov, V.I.: Homological dimension theory, Russ. Math. Surveys 23 (1968), 5.1–45.

    Article  MathSciNet  MATH  Google Scholar 

  • -, Liseikin, V.D.: The softness of an inductive limit of soft sheaves, Siberian Math. J. 12 (1971), 820–821.

    Article  MathSciNet  MATH  Google Scholar 

  • Lisitsa, Y.: Extension of continuous maps and the factorisation theorem, Siberian Math. J. 14 (1973), 90–96.

    Article  Google Scholar 

  • Macdonald, I.G.: Algebraic geometry, Benjamin, New York (1968).

    Google Scholar 

  • MacLane, S.: Homology, Springer-Verlag, Heidelberg (1963).

    Book  MATH  Google Scholar 

  • -: Categories for the working mathematician, Springer-Verlag, Heidelberg (1971).

    MATH  Google Scholar 

  • Michael, E.: Cuts, Acta Math. 111 (1964), 1–36.

    Article  MathSciNet  MATH  Google Scholar 

  • Mioduszewski, J., Rudolf, L.: H-closed and extremally disconnected Hausdorff spaces, Dissertationes Mathematicae 66, (1969) 1–55.

    MathSciNet  MATH  Google Scholar 

  • Morita, K.: On the dimension of the product of Tychonoff spaces General topology and its applications 3 (1973) 125–134.

    Article  MathSciNet  MATH  Google Scholar 

  • Mulvey, C.: Intuitionistic algebra and representations of rings Mem. Amer. Math. Soc. 148 (1974), 3–57.

    MathSciNet  MATH  Google Scholar 

  • Mulvey, C.: Compact ringed spaces, (1976) (preprint).

    Google Scholar 

  • Nagami, K.: Mappings defined on O-dimensional spaces and dimension theory, J. Math. Soc. Japan 14 (1962) 101–117.

    Article  MathSciNet  MATH  Google Scholar 

  • -: Dimension theory, Academic Press, New York (1970).

    MATH  Google Scholar 

  • Pasynkov, B.A.: Partial topological products, Trans. Moscow Math. Soc. 13, (1965) 153–272.

    MathSciNet  MATH  Google Scholar 

  • -: On a formula of Hurewicz, Vestnik Mosk. Gos. Univ. ser. 1. Math. Mech. 20 (1965), (4) 3–5.

    MathSciNet  MATH  Google Scholar 

  • Pears, A.R.: Dimension theory of general spaces Cambridge (1975).

    Google Scholar 

  • -, Mack, J.: Closed covers, dimension, and quasi-order spaces, Proc. London Math. Soc. (3) 29 (1974), 289–316.

    Article  MathSciNet  MATH  Google Scholar 

  • Ponomarev, V.: Projective spectra and continuous mappings of paracompacta, Amer. Math. Soc. Translat. Ser. 2 39 (1964).

    Google Scholar 

  • Rainwater, J.: A note on projective resolutions, Proc. Amer. Math. Soc. 20 (1959), 734–735.

    Article  MathSciNet  MATH  Google Scholar 

  • Ringel, C.M.: Diagonalisierungspaare I, Math. Zeitschrift 117 (1970), 249–266.

    Article  MathSciNet  MATH  Google Scholar 

  • -: ibid., ibid. 122 (1971), 10–32.

    Article  MathSciNet  MATH  Google Scholar 

  • Scott, D.S., Fourman, M.P.: Sheaves and logic preprint (Oxford, 1975).

    Google Scholar 

  • Shukla, W., Srivastava, A.: Local reflectivity+stable reflectivity=reflectivity, Gen. top. and its applications 5 (1975), 61–68.

    Article  MathSciNet  MATH  Google Scholar 

  • Sklyarenko, E.G.: A theorem on maps which lower dimension Bull. Acad. Polon. des Sciences, ser. Sci., Math., etc. 10 (1962), 429–432.

    MATH  Google Scholar 

  • -: Some applications of the theory of sheaves in general topology, Russ. Math. Surveys 19 (1964), 6.41–62.

    Article  MathSciNet  Google Scholar 

  • Skordev, G.S.: On resolutions of continuous mappings, Math. USSR Sbornik 11 (1970), 491–506.

    Article  MATH  Google Scholar 

  • -: Resolutions corresponding to closed mappings, ibid. 15 (1971), 227–240.

    Article  MATH  Google Scholar 

  • Strecker, G.: Component properties and factorisations, Mathematical Centre Tracts 52 Amsterdam (1974), 123–140.

    MathSciNet  Google Scholar 

  • Strecker, G.: Perfect morphisms these proceedings (1976?).

    Google Scholar 

  • Whyburn, G.T.: Analytic topology, Amer. Math. Soc. Colloquium Publ. 28 (1963).

    Google Scholar 

  • Wraith, G.C., et al.: Model Theory and Topoi Lecture Notes in Mathematics 445, Springer-Verlag (1975).

    Google Scholar 

  • Wyler, O.: A characterisation of regularity in topology, Proc. Amer. Math. Soc. 29 (1971), 588–590.

    Article  MathSciNet  MATH  Google Scholar 

  • Zakharov, V.K.: Isomorphism of the homology groups of a locally compact space and groups of module extensions Siberian Math. J. 15 (1974), 670–673.

    Article  MATH  Google Scholar 

  • Zarelua, A.V.: Finite-to-one mappings of topological spaces and cohomology manifolds, Siberian Math. J. 10 (1969), 45–63.

    Article  MathSciNet  MATH  Google Scholar 

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  1. St. Andrews University, Fife, Scotland

    Roy Dyckhoff

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  1. Roy Dyckhoff
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Ernst Binz Horst Herrlich

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Dyckhoff, R. (1976). Categorical methods in dimension theory. In: Binz, E., Herrlich, H. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 540. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080861

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  • DOI: https://doi.org/10.1007/BFb0080861

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