Bulletin (New Series) of the American Mathematical Society
- Bull. Amer. Math. Soc. (N.S.)
- Volume 8, Number 1 (1983), 41-53.
The point of pointless topology
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Article information
Source
Bull. Amer. Math. Soc. (N.S.), Volume 8, Number 1 (1983), 41-53.
Dates
First available in Project Euclid: 4 July 2007
Permanent link to this document
https://projecteuclid.org/euclid.bams/1183550014
Mathematical Reviews number (MathSciNet)
MR682820
Zentralblatt MATH identifier
0499.54002
Subjects
Primary: 06A23 18B30: Categories of topological spaces and continuous mappings [See also 54-XX] 54A05: Topological spaces and generalizations (closure spaces, etc.)
Secondary: 01A60: 20th century 06D05: Structure and representation theory 18B25: Topoi [See also 03G30]
Citation
Johnstone, Peter T. The point of pointless topology. Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 1, 41--53. https://projecteuclid.org/euclid.bams/1183550014
References
- 1. B. Banaschewski, The duality of distributive continuous lattices, Canad. J. Math. 32 ( 1980), 385-394.Zentralblatt MATH: 0434.06011
Mathematical Reviews (MathSciNet): MR571932
Digital Object Identifier: doi:10.4153/CJM-1980-030-3 - 2. B. Banaschewski, Extension of invariant linear functionals: Hahn-Banach in the topos of M-sets, J. Pure Appl. Algebra 17 (1980), 227-248.Zentralblatt MATH: 0453.18003
Mathematical Reviews (MathSciNet): MR579085
Digital Object Identifier: doi:10.1016/0022-4049(80)90047-X - 3. B. Banaschewski and C. J. Mulvey, Stone-Čech compactification of locales, I, Houston J. Math. 6 (1980), 301-312.
- 4. J. Bénabou, Treillis locaux et paratopologies, Séminaire Ehresmann (Topologie et Géométrie Différentielle), 1re année (1957-58), exposé 2.
- 5. C. H. Dowker and D. Papert, Quotient frames and subspaces, Proc. London Math. Soc. 16 (1966), 275-296.Zentralblatt MATH: 0136.43405
Mathematical Reviews (MathSciNet): MR202648
Digital Object Identifier: doi:10.1112/plms/s3-16.1.275 - 6. C. H. Dowker and D. Papert, On Urysohn's lemma, General Topology and its Relations to Modern Analysis and Algebra (Proc. Prague Symposium, 1966), Academia, Prague, 1967, pp. 111-114.
- 7. C. H. Dowker and D. Strauss, Separation axioms for frames, Colloq. Math. Soc. János Bolyai 8 (1972), 223-240.
- 8. C. H. Dowker and D. Strauss, Paracompact frames and closed maps, Sympos. Math. 16 (1975), 93-116.
- 9. C. H. Dowker and D. Strauss, Sums in the category of frames, Houston J. Math. 3 (1977), 7-15.
- 10. R. Dyckhoff, Factorization theorems and projective spaces in topology, Math. Z. 127 (1972), 256-264.Zentralblatt MATH: 0226.54009
Mathematical Reviews (MathSciNet): MR312452
Digital Object Identifier: doi:10.1007/BF01114928 - 11. R. Dyckhoff, Categorical methods in dimension theory, Categorical Topology (Proc. Mannheim Conf., 1975), Lecture Notes in Math., vol. 540, Springer-Verlag, Berlin and New York, 1976, pp. 220-242.
- 12. C. Ehresmann, Gattungen von lokalen Strukturen, Jber. Deutsch. Math.-Verein. 60 (1957), 59-77.
- 13. C. Ehresmann, Catégories topologiques et catégories diffèrentiables, Colloq. Géom. Diff. Globale (Bruxelles), Centre Belge Rech. Math., Louvain, 1959, pp. 137-150.
- 14. J. Fingerman, The historical and philosophical significance of the emergence of point-set topology, Ph.D. thesis, Univ. of Chicago, 1981.
- 15. M. P. Fourman and J. M. E. Hyland, Sheaf models for analysis, Applications of Sheaves (Proc. Durham Symposium, 1977), Lecture Notes in Math., vol. 753, Springer-Verlag, Berlin and New York, 1979, pp. 280-301.
- 16. R. H. Fox, Covering spaces with singularities, Algebraic Topology (Sympos. in honor of S. Lefschetz), Princeton Univ. Press, Princeton, N. J., 1957, pp. 243-257.
- 17. M. Fréchet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 (1906), 1-71.
- 18. A. M. Gleason, Projective topological spaces, Illinois J. Math. 2 (1958), 482-489.Zentralblatt MATH: 0083.17401
Mathematical Reviews (MathSciNet): MR121775
Project Euclid: euclid.ijm/1255454110 - 19. R. J. Grayson, Constructive properties of complete Heyting algebras and related structures, preprint (1982).Mathematical Reviews (MathSciNet): MR674673
Zentralblatt MATH: 0495.03040
Digital Object Identifier: doi:10.1016/0003-4843(82)90010-9 - 20. J. D. Halpern, The independence of the axiom of choice from the Boolean prime ideal theorem, Fund. Math. 55 (1964), 57-66.
- 21. F. Hausdorff, Grundzüge der Mengenlehre, Veit & Co., Leipzig, 1914.Mathematical Reviews (MathSciNet): MR31025
- 22. M. Hochster, Prime ideal structure in commutative rings, Trans. Amer. Math. Soc. 142 (1969), 43-60.Zentralblatt MATH: 0184.29401
Mathematical Reviews (MathSciNet): MR251026
Digital Object Identifier: doi:10.1090/S0002-9947-1969-0251026-X - 23. K. H. Hofmann and J. D. Lawson, The spectral theory of distributive continuous lattices, Trans. Amer. Math. Soc. 246 (1978), 285-310.Zentralblatt MATH: 0402.54043
Mathematical Reviews (MathSciNet): MR515540
Digital Object Identifier: doi:10.1090/S0002-9947-1978-0515540-7 - 24. J. M. E. Hyland, Function-spaces in the category of locales, Continuous Lattices (Proc. Bremen workshop, 1979), Lecture Notes in Math., vol. 871, Springer-Verlag, Berlin and New York, 1981, pp. 264-281.Zentralblatt MATH: 0483.54005
- 25. J. R. Isbell, Atomless parts of spaces, Math. Scand. 31 (1972), 5-32.
- 26. J. R. Isbell, Product spaces in locales, Proc. Amer. Math. Soc. 81 (1981), 116-118.Zentralblatt MATH: 0473.54027
Mathematical Reviews (MathSciNet): MR589150
Digital Object Identifier: doi:10.1090/S0002-9939-1981-0589150-5 - 27. I. M. James, Ex-homotopy theory. I, Illinois J. Math. 15 (1971), 324-337.Zentralblatt MATH: 0225.55012
Mathematical Reviews (MathSciNet): MR296945
Project Euclid: euclid.ijm/1256052718 - 28. I. M. James, Alternative homotopy theories, Enseign. Math. (2) 23 (1977), 221-237.
- 29. P. T. Johnstone, Topos theory, L.M.S. Math. Mono., no. 10, Academic Press, London, 1977.
- 30. P. T. Johnstone, Open maps of toposes, Manuscripta Math. 31 (1980), 217-247.Zentralblatt MATH: 0433.18002
Mathematical Reviews (MathSciNet): MR576498
Digital Object Identifier: doi:10.1007/BF01303275 - 31. P. T. Johnstone, The Gleason cover of a topos. I, J. Pure Appl. Algebra 19 (1980), 171-192.Zentralblatt MATH: 0445.18004
Mathematical Reviews (MathSciNet): MR593253
Digital Object Identifier: doi:10.1016/0022-4049(80)90100-0 - 32. P. T. Johnstone, The Gleason cover of a topos. II, J. Pure Appl. Algebra 22 (1981), 229-247.Zentralblatt MATH: 0445.18005
Mathematical Reviews (MathSciNet): MR629332
Digital Object Identifier: doi:10.1016/0022-4049(81)90100-6 - 33. P. T. Johnstone, Tychonoff's theorem without the axiom of choice, Fund. Math. 113 (1981), 21-35.
- 34. P. T. Johnstone, Factorization theorems for geometric morphisms. II, Categorical Aspects of Topology and Analysis (Proc. Carleton Conf., 1980), Lecture Notes in Math., vol. 915, Springer-Verlag, Berlin and New York, 1982, pp. 216-233.Zentralblatt MATH: 0477.18006
Mathematical Reviews (MathSciNet): MR659894
Digital Object Identifier: doi:10.1007/BFb0092882 - 35. P. T. Johnstone, Stone spaces, Cambridge Univ. Press, Cambridge, 1982.
- 36. P. T. Johnstone, The Vietoris monad on the category of locales (in preparation).
- 37. A. Joyal and M. Tierney, An extension of the Galois theory of Grothendieck (to appear).
- 38. F. C. Kirwan, Uniform locales, Part III dissertation, Univ. of Cambridge, 1981.
- 39. K. Kuratowski, Sur l'opération Ā de l'analysis situs, Fund. Math. 3 (1922), 182-199.
- 40. W. Kuyk, Complementarity in mathematics, Math, and its applications, vol. 1, Reidel, Dordrecht, 1977.
- 41. F. W. Lawvere, Continuously variable sets: Algebraic geometry = geometric logic (Logic Colloq., 1973), Studies in Logic and the Foundations of Math., vol. 80, North-Holland, Amsterdam, 1975, pp. 135-156.
- 42. J. Leray, L'anneau spectral et l'anneau filtré d'homologie d'un espace localement compact et d'une application continue, J. Math. Pures Appl. 29 (1950), 1-80.
- 43. F. E. J. Linton, Some aspects of equational categories, Categorical Algebra (Proc. La Jolla Conf., 1965), Springer-Verlag, Berlin and New York, 1966, pp. 84-94.
- 44. J. Łoš and C. Ryll-Nardzewski, On the application of Tychonoff's theorem in mathematical proofs, Fund. Math. 38 (1951), 233-237.
- 45. S. Mac Lane, The influence of M. H. Stone on the origins of category theory, Functional Analysis and Related Fields, Springer-Verlag, Berlin and New York, 1970, pp. 228-241.
- 46. S. Mac Lane, Sets, topoi and internal logic in categories (Logic Colloq., 1973), Studies in Logic and the Foundations of Math., vol. 80, North-Holland, Amsterdam, 1975, pp. 119-134.
- 47. J. C. C. McKinsey and A. Tarski, The algebra of topology, Ann. of Math. (2) 45 (1944), 141-191.Zentralblatt MATH: 0060.06206
Mathematical Reviews (MathSciNet): MR9842
Digital Object Identifier: doi:10.2307/1969080 - 48. J. C. C. McKinsey and A. Tarski, On closed elements in closure algebras, Ann. of Math. (2) 47 ( 1946), 122-162.Zentralblatt MATH: 0060.06207
Mathematical Reviews (MathSciNet): MR15037
Digital Object Identifier: doi:10.2307/1969038 - 49. J. Nagata, Modern dimension theory, Noordhoff, Groningen, 1965.Zentralblatt MATH: 0129.38304
- 50. S. B. Niefield, Exactness and projectivity, Category Theory (Proc. Gummersbach Conf., 1981), Lecture Notes in Math., Springer-Verlag, Berlin and New York, (to appear).Zentralblatt MATH: 0497.18013
Mathematical Reviews (MathSciNet): MR682960
Digital Object Identifier: doi:10.1007/BFb0066902 - 51. G. Nöbeling, Grundlagen der analytischen Topologie, Die Grundlehren der math. Wissenschaften, Band 72, Springer-Verlag, Berlin and New York, 1954.
- 52. D. Papert, Lattices of functions, measures and point-sets, Ph.D. thesis, Univ. of Cambridge, 1958.
- 53. S. Papert, The lattices of logic and topology, Ph.D. thesis, Univ. of Cambridge, 1959.
- 54. H. Simmons, A couple of triples, Topology Appl. 13 (1982), 201-223.Zentralblatt MATH: 0484.18005
Mathematical Reviews (MathSciNet): MR644114
Digital Object Identifier: doi:10.1016/0166-8641(82)90021-9 - 55. M. H. Stone, Boolean algebras and their applications to topology, Proc. Nat. Acad. Sci. U.S.A. 20 (1934), 197-202.Zentralblatt MATH: 0010.08104
- 56. M. H. Stone, The theory of representations for Boolean algebras, Trans. Amer. Math. Soc. 40 (1936), 37-111.
- 57. M. H. Stone, Topological representation of distributive lattices and Brouwerian logics, Časopis pešt. mat. fys. 67 (1937), 1-25.
- 58. L. Vietoris, Bereiche zweiter Ordnung, Monatsh. für Math, und Physik 32 (1922), 258-280.
- 59. H. Wallman, Lattices and topological spaces, Ann. of Math. (2) 39 (1938), 112-126.Zentralblatt MATH: 0018.33202
Mathematical Reviews (MathSciNet): MR1503392
Digital Object Identifier: doi:10.2307/1968717 - 60. S. Willard, General topology, Addison-Wesley, Reading, Mass., 1970.
- 61. G. C. Wraith, Galois theory in a topos, J. Pure Appl. Algebra 19 (1980), 401-410.Zentralblatt MATH: 0441.18008
Mathematical Reviews (MathSciNet): MR593261
Digital Object Identifier: doi:10.1016/0022-4049(80)90108-5 - 62. G. C. Wraith, Localic groups, Cahiers Topologie Géom. Différentielle 22 (1981), 61-66.
- 63. A. V. Zarelua, Sheaf theory and zero-dimensional mappings, Applications of Sheaves (Proc. Durham Sympos., 1977), Lecture Notes in Math., vol. 753, Springer-Verlag, Berlin and New York, 1979, pp. 768-779.
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