Epireflections which are completions

G. C. L. Brummer; E. Giuli; H. Herrlich

Cahiers de Topologie et Géométrie Différentielle Catégoriques (1992)

  • Volume: 33, Issue: 1, page 71-93
  • ISSN: 1245-530X

How to cite


Brummer, G. C. L., Giuli, E., and Herrlich, H.. "Epireflections which are completions." Cahiers de Topologie et Géométrie Différentielle Catégoriques 33.1 (1992): 71-93. <http://eudml.org/doc/91492>.

author = {Brummer, G. C. L., Giuli, E., Herrlich, H.},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {firm epireflection; weak injectivity; saturated object; topological category; reflective subcategory},
language = {eng},
number = {1},
pages = {71-93},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Epireflections which are completions},
url = {http://eudml.org/doc/91492},
volume = {33},
year = {1992},

AU - Brummer, G. C. L.
AU - Giuli, E.
AU - Herrlich, H.
TI - Epireflections which are completions
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 1992
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 33
IS - 1
SP - 71
EP - 93
LA - eng
KW - firm epireflection; weak injectivity; saturated object; topological category; reflective subcategory
UR - http://eudml.org/doc/91492
ER -


  1. 1 P. Alexandroff and P. Urysohn, Zur Theorie der topologischen Räume, Math. Ann.92 (1924) 258-266. Zbl50.0128.06MR1512213JFM50.0128.06
  2. 2 P.D. Bacsich, An epi-reflector for universal theories, Canad. Math. Bull.16 (1973) 167-171. Zbl0265.08008MR335589
  3. 3 B. Banaschewski, Projective covers in categories of topological spaces and topological algebras, General Topology and its Relations to Modern Analysis and Algebra (Proc. Conf. Kanpur 1968, Academia, Prague-Academic Press, New York, 1971) pp. 63-91. Zbl0227.54005MR284388
  4. 4 B. Banaschewski, G .C .L . Brümmer and K.A. Hardie, Biframes and bispaces, Quaestiones Math.6 (1983) 13-25. Zbl0513.06005MR700237
  5. 5 B. Banaschewski and G. Bruns, Injective hulls in the category of distributive lattices, J. Reine Angew. Math.232 (1968) 102-109. Zbl0186.30606MR237607
  6. 6 B. Banaschewski and H. Herrlich, Subcategories defined by implications, Houston J. Math.2 (1977) 149-171. Zbl0344.18002MR401867
  7. 7 H.L. Bentley and H. Herrlich, Completion as reflection, Comment. Math. Univ. Carolin19 (1978) 541-568. Zbl0407.54020MR508960
  8. 8 H.L. Bentley and H. Herrlich, Completeness for nearness spaces, Math. Centre Tracts (Amsterdam) 115 (1979) pp. 29-40. Zbl0419.54014MR565823
  9. 9 M.P. Berri, J.R. Porter and R.M. Stephenson, A survey of minimal topological spaces, General Topology and its Relations to Modern Analysis and Algebra (Proc. Conf. Kanpur 1968, Academia, Prague-Academic Press, New York, 1971) pp. 93-114. Zbl0235.54018MR278254
  10. 10 G. Birkhoff, The meaning of completeness, Ann. Math.38 (1937) 57-60. Zbl0016.08503MR1503324
  11. 11 N. Bourbaki, Eléments de mathematique: Livre III: Topologie Générale, Chapitre 3 (Hermann, Paris, 1960). Zbl0102.27104
  12. 12 H.-P. Butzamann and G. Kneis, Cech-Stone compactifications of pseudotopological spaces, Math. Nachr.128 (1986) 259-264. Zbl0602.54027MR855961
  13. 13 G.C.L. Brümmer, On the non-unique extension of topological to bitopological properties, Categorical aspects of Topology and Analysis, Lecture Notes in Math.915 (Springer, Berlin, 1982) pp. 50-67. Zbl0491.54025MR659883
  14. 14 A. Császár, Fondements de la topologie générale, (Akademiai Kiado, Budapest, 1960). Zbl0091.35702MR113205
  15. 15 A. Császár, Foundations of general topology (Revised and extended edition of [14]) (Pergamon Press, Oxford, 1963). Zbl0108.35304MR157340
  16. 16 D. Dikranjan and e. Giuli, Urysohn-closed spaces: old and new, unpublished manuscript, University of L'Aquila, 1984. 
  17. 17 D. Dikranjan and E. Giuli, Ordinal invariants and epimorphisms in categories of weak Hausdorff spaces, Comment. Math. Univ. Carolin.27 (1986) 395-417. Zbl0627.54005MR857557
  18. 18 D. Dikranjan and E. Giuli, Closure operators I, Topology Appl.27 (1987) 129-143. Zbl0634.54008MR911687
  19. 19 D. Dikranjan and E. Giuli, S(n)-θ-closed spaces, Topology Appl.28 (1988) 59-74. Zbl0658.54015
  20. 20 D. Dikranjan and E. Giuli, Epimorphisms in categories of convergence spaces, preprint, University of L'Aquila, 1988. Zbl0658.54015MR927282
  21. 21 D. Dikranjan and E. Giuli, Epimorphisms and completeness in categories of modules, preprint, University of L'Aquila, 1990. 
  22. 22 D. Dikranjan, E. Giuli and W. Tholen, Closure operators II, in: Categorical Topology (Proc. Conf., Prague, 1988), 297-335, World Sci. Publ., Singapore, 1989. MR1047909
  23. 23 H. Ehrig and H. Herrlich, The construct PRO of projection spaces: its internal structure, in: Categorical methods in Computer Science, Lecture Notes in Computer Science393 (Springer-Verlag, Berlin, 1989), 286-293. MR1048368
  24. 24 P. Fletcher and W.F. Lindgren, Quasi-uniform spaces, (Marcel Dekker, New York, 1982). Zbl0501.54018MR660063
  25. 25 C.R.A. Gilmour, Realcompact Alexandroff spaces and regular σ- frames. Thesis, Univ. Cape Town, 1981. Reprinted as Math. MonographsUniv. Cape Town, no. 3, Cape Town, 1985. Zbl0601.54019
  26. 26 E. Giuli, On m-projection spaces. Preprint, University of L'Aquila, 1989. Zbl0840.18003
  27. 27 E. Giuli and M. Hušek, A diagonal theorem for epireflective subcategories of Top and co-well-poweredness, Ann. Mat. Pura Appl.145 (1986) 337-346. Zbl0617.54006MR886716
  28. 28 E. Giuli and S. Salbany, 2T0-spaces and closure operators, Seminarberichte Fach. Math. und Inf. (Fern Universität Ha-gen) 28 (1988) 11-40. 
  29. 29 E. Giuli and P. Simon, Spaces in which every bounded subset is Hausdorff, Topology Appl.37 (1990), 267-274. Zbl0719.54009MR1082937
  30. 30 H. Gordon, Rings of functions determined by zero-sets, Pacific J. Math.36 (1971) 133-157. Zbl0185.38803MR320996
  31. 31 A.W. Hager, Some nearly fine uniform spaces, Proc. London Math. Soc.28 (1974) 537-546. Zbl0284.54017MR397670
  32. 32 H. Herrlich, Categorical Topology, Gen. Topology Appl.1 (1971) 1-15. Zbl0215.51501MR283744
  33. 33 H. Herrlich, Cartesian closed topological categories, Math. Colloq. Univ. Cape Town9 (1974) 1-16. Zbl0318.18011MR460414
  34. 34 H. Herrlich, Categorical Topology 1971-1981, General Topology and its Applications to Modern Analysis and Algebra V, Proc. Symp. Prague1981, (Heldermann Verlag, Berlin1982) pp. 272-383. Zbl0502.54001MR698425
  35. 35 H. Herrlich, Topological structures and injectivity, Rend. Circ. Mat. Palermo Suppl. 12 (1986) 87-92. Zbl0589.54018MR853149
  36. 36 H. Herrlich and G.E. Strecker, Category Theory (Heldermann Verlag, 2a Ed., 1979). Zbl0437.18001MR571016
  37. 37 R.-E. Hoffmann, (E, M)-universally topological functors, Habilitationsschrift, Univ. Düsseldorl, 1974. 
  38. 38 R.-E. Hoffmann, Topological functors admitting generalized Cauchy-completions, Categorical Topology, Lecture Notes in Math.540 (Springer, Berlin, 1976) pp. 286-344. Zbl0421.18002MR644648
  39. 39 J.M. Howie and J. Isbell, Epimorphisms and dominions II, J. Algebra6 (1967) 7-21. Zbl0211.33303MR209203
  40. 40 H. Hogbe-Nlend, Théorie des bornologies et applications, Lecture Notes in Math.213 (Springer-Verlag, 1971). Zbl0225.46005MR625157
  41. 41 J.R. Isbell, Uniform Spaces, (Amer. Math. Soc., Providence RI, 1964). Zbl0124.15601
  42. 42 J.R. Isbell, Epimorphisms and dominions, Proc. Confer. Categorical Algebra (La Jolla, 1965) (Springer, Berlin, 1966) pp. 232-246. Zbl0194.01601MR209202
  43. 43 J.C. Kelly, Bitopological spaces, Proc. London Math. Soc. (3) 13 (1963) 71-89. Zbl0107.16401MR143169
  44. 44 E.W. Kiss, L. Marki, P. Prohle and W. Tholen, Compendium on amalgamation, congruence extension, epimorphisms, residual smallness and injectivity, Studia Sci. Math. Hungar.18 (1983) 79-141. Zbl0549.08001MR759319
  45. 45 Th. Marny, On epireflective subcategories of topological categories, General Topology Appl.10 (1979) 175-181. Zbl0415.54007MR527843
  46. 46 G. Preuss, Some categorical aspects of simplicial complexesQuaestiones Math.6 (1983) 313-322. Zbl0535.18007MR734652
  47. 47 S. Salbany, Bitopological spaces, compactifications and completions, Ph.D. thesis, Univ. Cape Town, 1970. Reprinted as Math. Monographs Univ. Cape Town, no. 1, 1974. Zbl0353.54021MR425919
  48. 48 J. Schröder, The category of Urysohn spaces is not co-well-powered, Topology Appl.16 (1983) 237-241. Zbl0534.54004MR722116
  49. 49 D. Scott, Continuous lattices, Lecture Notes in Math.274 (Springer, Berlin, 1972) pp. 97-136. Zbl0239.54006MR404073
  50. 50 M. Sobral, Absolutely closed spaces and categories of algebras, Portugaliae Math.47 (1990), 341-351. Zbl0732.18001MR1090472
  51. 51 R.M. Stephenson, Jr., Some unsolved problems concerning P-minimal and P-closed spaces, in: Proc. Charlotte Topol. Conf. (Academic Press, New York, 1974) 249-257. Zbl0348.54012MR448305
  52. 52 W. Tholen, Injective objects and cogenerating sets, J. Algebra73 (1981) 139-155. Zbl0487.18014MR641637
  53. 53 A. Weil, Sur les espaces a structure uniforme et sur la topologie générale, Hermann, Paris, 1937. Zbl0019.18604
  54. 54 S. Weck-Schwarz, T0-objects and separated objects in topological categories, preprint, 1988. MR1123910
  55. 55 S. Weck-Schwarz, Cartesisch abgeschlossene monotopologische Hüllen and die Rolle der T0 -Reflexion. Dissertation, Univ. Hannover1988. Zbl1077.54500

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