Keywords
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Aleksandroff, P.S.: On some basic directions in general topology, Russian Math. Surveys 19 (1964), 6.1–39.
-: corrections to above, ibid 20 (1965) 1.177–178.
Banaschewski, B.: Projective covers in categories of topological spaces and topological algebras, Proc. Kanpur Top. Conference (1968), Academia, Prague, 63–91.
Barr, M., Beck, J.: Homology and standard constructions, Lecture Notes in Mathematics 80, Springer-Verlag (1969), 245–335.
Bartik, V.: Aleksandrov-Čech cohomology and mappings into Eilenberg-MacLane polyhedra, Math. USSR Sbornik 5 (1968), 221–228.
Benabou, J.: Introduction to bicategories, Lecture Notes in Mathematics, 47, Springer-Verlag (1967), 1–77.
Blaszczyk, A.: A factorisation theorem and its application to extremally disconnected resolutions. Colloq. Math. 28 (1974), 33–40.
-: Extremally disconnected resolutions of T 0 -spaces, ibid 32 (1974a), 57–68.
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.
-: The homological theory of dimension, Russian Math. Surveys 21 (1966), 7–12.
Bredon, G.E.: Sheaf theory, McGraw-Hill, New York (1967).
Collins, P.J.: Concordant mappings and the concordant-dissonant factorisation of an arbitrary continuous function, Proc. Amer. Math. Soc. 27 (1971), 587–591.
-: Connection properties in topological spaces, Mathematika Balkancia, 1, (1971a) 44–51.
Diers, Y.: Complétion monadique, C.R. Acad. Sci. Paris 276 (1973) A1397–A1400.
Duskin, J.: Simplicial methods and the interpretation of “triple” cohomology, Mem. Amer. Math. Soc. 163 (1975).
Dyckhoff, R.: Factorisation theorems and projective spaces in topology Math. Zeitschrift 127 (1972), 256–264.
-: Perfect light maps as inverse limits, Quart. J. Math. Oxford (2), 25 (1974), 441–449.
Dyckhoff, R.: Topics in general topology: bicategories, projective covers, perfect mappings and resolutions of sheaves, thesis, Oxford (1974a).
-: Projective resolutions of topological spaces J. Pure and Applied Algebra 7 (1976), 115–119.
Dyckhoff, R.: Categorical Cuts, to appear (1976a).
Eilenberg, S.: Sur les transformations continues d'espaces metriques compacts, Fund. Math. 22 (1934), 292–296.
Filippov, V.: On the dimension of closed mappings, Sov. Math. Dokl. 13 (1972), 895–900.
Fourman, M.P.: Comparaison des réelles d'un topos: structures lisses sur un topos élémentaire Amines 1975, to appear in Cah. Top. Geom. Diff.
Fourman, M.P.: The logic of topoi, Handbook of mathematical logic (ed. Barwise), North Holland (1976).
Freyd, P.: Aspects of topoi, Bull. Austral. Math. Soc., 7 (1972), 1–76.
Gillman, L., Jerison, M.: Rings of continuous functions, Van Nostrand, Princeton (1960).
Gleason, A.: Projective topological spaces, Illinois J. Math. 2 (1958), 482–9.
Godement, R.: Théorie des faisceaux, Hermann Paris (1964).
Gonshor, H.: Projective covers as subquotients of enlargements, Israel J. of Math. 14 (1973), 257–261.
Goto, T.: Homotopical cohomology groups of paracompact spaces, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A, 9 (1967), 21–27.
Gray, J.W.: Formal Category Theory II, Springer Lecture Notes, to appear (1975?).
Grothendieck, A., et al.: Théorie des topos et cohomologie etale des schemas, (SGA4), Lecture notes in mathematics 269, Springer-Verlag (1972).
Grothendieck, A., et al.: ibid. Théorie des topos et cohomologie etale des schemas, (SGA4), Lecture notes in mathematics 270 (1972a).
Hager, A.W.: The projective resolution of a compact space, Proc. Amen. Math. Soc. 28 (1971) 262–266.
Harris, D.: Katetov extension as a functor, Math. Ann. 193 (1971), 171–175.
Henriksen, M., Isbell, J.R.: Some properties of compactifications, Duke Math. J. 25 (1958), 83–105.
Henriksen, M., Jerison, M.: Minimal projective extensions of compact spaces, Duke Math. J. 32, (1965), 291–295.
Herrlich, H.: Topologische Reflexionen und Coreflexionen Lecture notes in Mathematics, 78, Springer-Verlag, Heidelberg (1968).
-: Categorical topology, General topology and its applications 1, (1971) 1–15.
Herrlich, H.: A generalisation of perfect maps, Proc. Third Prague Top. Symposium 1971, Academia Prague (1973) 187–192.
-: 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).
Huber, P.J.: Homotopical cohomology and Čech cohomology, Math. Ann. 144 (1961), 73–76.
Hurewicz and Wallman, Dimension theory, Princeton (1948).
Isbell, J.R.: Subobjects, adequacy, completeness, and categories of algebras, Rozprawy Mat. 38, (1963) 1–32.
Johnstone, P.: Aspects of internal category theory, thesis, Cambridge (1974).
Kennison, J.F.: Full reflective subcategories and generalised covering spaces, Illinois J. Math. 12, (1968) 353–365.
Kock, A., Wraith, G.C.: Elementary topoi, Aarhus lecture notes, 30 (1971).
Kulpa, W.: Factorisation and inverse expansion theorems for uniformities, Colloq. Math. 21, (1970) 217–227.
Kuz'minov, V.I.: Homological dimension theory, Russ. Math. Surveys 23 (1968), 5.1–45.
-, Liseikin, V.D.: The softness of an inductive limit of soft sheaves, Siberian Math. J. 12 (1971), 820–821.
Lisitsa, Y.: Extension of continuous maps and the factorisation theorem, Siberian Math. J. 14 (1973), 90–96.
Macdonald, I.G.: Algebraic geometry, Benjamin, New York (1968).
MacLane, S.: Homology, Springer-Verlag, Heidelberg (1963).
-: Categories for the working mathematician, Springer-Verlag, Heidelberg (1971).
Michael, E.: Cuts, Acta Math. 111 (1964), 1–36.
Mioduszewski, J., Rudolf, L.: H-closed and extremally disconnected Hausdorff spaces, Dissertationes Mathematicae 66, (1969) 1–55.
Morita, K.: On the dimension of the product of Tychonoff spaces General topology and its applications 3 (1973) 125–134.
Mulvey, C.: Intuitionistic algebra and representations of rings Mem. Amer. Math. Soc. 148 (1974), 3–57.
Mulvey, C.: Compact ringed spaces, (1976) (preprint).
Nagami, K.: Mappings defined on O-dimensional spaces and dimension theory, J. Math. Soc. Japan 14 (1962) 101–117.
-: Dimension theory, Academic Press, New York (1970).
Pasynkov, B.A.: Partial topological products, Trans. Moscow Math. Soc. 13, (1965) 153–272.
-: On a formula of Hurewicz, Vestnik Mosk. Gos. Univ. ser. 1. Math. Mech. 20 (1965), (4) 3–5.
Pears, A.R.: Dimension theory of general spaces Cambridge (1975).
-, Mack, J.: Closed covers, dimension, and quasi-order spaces, Proc. London Math. Soc. (3) 29 (1974), 289–316.
Ponomarev, V.: Projective spectra and continuous mappings of paracompacta, Amer. Math. Soc. Translat. Ser. 2 39 (1964).
Rainwater, J.: A note on projective resolutions, Proc. Amer. Math. Soc. 20 (1959), 734–735.
Ringel, C.M.: Diagonalisierungspaare I, Math. Zeitschrift 117 (1970), 249–266.
-: ibid., ibid. 122 (1971), 10–32.
Scott, D.S., Fourman, M.P.: Sheaves and logic preprint (Oxford, 1975).
Shukla, W., Srivastava, A.: Local reflectivity+stable reflectivity=reflectivity, Gen. top. and its applications 5 (1975), 61–68.
Sklyarenko, E.G.: A theorem on maps which lower dimension Bull. Acad. Polon. des Sciences, ser. Sci., Math., etc. 10 (1962), 429–432.
-: Some applications of the theory of sheaves in general topology, Russ. Math. Surveys 19 (1964), 6.41–62.
Skordev, G.S.: On resolutions of continuous mappings, Math. USSR Sbornik 11 (1970), 491–506.
-: Resolutions corresponding to closed mappings, ibid. 15 (1971), 227–240.
Strecker, G.: Component properties and factorisations, Mathematical Centre Tracts 52 Amsterdam (1974), 123–140.
Strecker, G.: Perfect morphisms these proceedings (1976?).
Whyburn, G.T.: Analytic topology, Amer. Math. Soc. Colloquium Publ. 28 (1963).
Wraith, G.C., et al.: Model Theory and Topoi Lecture Notes in Mathematics 445, Springer-Verlag (1975).
Wyler, O.: A characterisation of regularity in topology, Proc. Amer. Math. Soc. 29 (1971), 588–590.
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.
Zarelua, A.V.: Finite-to-one mappings of topological spaces and cohomology manifolds, Siberian Math. J. 10 (1969), 45–63.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0080861
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07859-3
Online ISBN: 978-3-540-38118-1
eBook Packages: Springer Book Archive