Johnstone, P. T. The Gleason cover of a topos. I. (English) Zbl 0445.18004 J. Pure Appl. Algebra 19, 171-192 (1980). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 14 Documents MSC: 18B25 Topoi 03B60 Other nonclassical logic 54G05 Extremally disconnected spaces, \(F\)-spaces, etc. Keywords:topos of sheaves; De Morgan’s law; Gleason cover; order-completion of the Dedekind real numbers; Hahn-Banach theorem in a topos Citations:Zbl 0083.174 PDFBibTeX XMLCite \textit{P. T. Johnstone}, J. Pure Appl. Algebra 19, 171--192 (1980; Zbl 0445.18004) Full Text: DOI References: [1] Banaschewski, B., Projective covers in categories of topological spaces and topological algebras, (Proc. Kanpur Topological Conference 1968 (1971), Academia: Academia Prague), 63-91 · Zbl 0227.54005 [2] Banaschewski, B., Extension of invariant linear functionals: Hahn-Banach in the topos of \(M\)-sets, J. Pure Applied Algebra, 17, 227-248 (1980) · Zbl 0453.18003 [3] Błaszcyk, A., Extremally disconnected resolutions of \(T_0\)-spaces, Colloq. Math., 32, 57-68 (1974) · Zbl 0301.54043 [4] Burden, C. W., The Hahn-Banach theorem in a category of sheaves, J. Pure Applied Algebra, 17, 25-34 (1980) · Zbl 0438.46051 [5] Flachsmeyer, J., Topologische Projektivräume, Math. Nachr., 26, 57-66 (1963) · Zbl 0136.19103 [6] Fourman, M. P.; Hyland, J. M.E., Sheaf models for analysis, Applications of Sheaves (Proc. L.M.S. Durham Symposium, 1977). Applications of Sheaves (Proc. L.M.S. Durham Symposium, 1977), Springer Lecture Notes in Math., 753, 280-301 (1979) · Zbl 0427.03028 [7] Gleason, A. M., Projective topological spaces, Ill. J. Math., 2, 482-489 (1958) · Zbl 0083.17401 [8] Grothendieck, A.; Verdier, J. L., Théorie des Topos (SGA 4, exposés I-IV), Springer Lecture Notes in Math., 269 (1972) · Zbl 0256.18008 [9] Iliadis, S., Absolutes of Hausdorff spaces, Soviet Math. Doklady, 4, 295-298 (1963) · Zbl 0134.41201 [10] Isbell, J. R., Injective envelopes of Banach spaces are rigidly attached, Bull. Amer. Math. Soc., 70, 727-729 (1964) · Zbl 0128.34503 [11] Johnstone, P. T., Topos Theory, (L.M.S. Mathematical Monographs no. 10 (1977), Academic Press: Academic Press London) · Zbl 0368.18001 [12] Johnstone, P. T., Rings, fields and spectra, J. Algebra, 49, 238-260 (1977) · Zbl 0369.13019 [13] Johnstone, P. T., Conditions related to De Morgan’s law, Applications of Sheaves (Proc. L.M.S. Durham Symposium, 1977). Applications of Sheaves (Proc. L.M.S. Durham Symposium, 1977), Springer Lecture Notes in Math., 753, 479-491 (1979) · Zbl 0445.03041 [14] Johnstone, P. T., Another condition equivalent to De Morgan’s law, Commun. Alg., 7, 1309-1312 (1979) · Zbl 0417.18002 [15] P.T. Johnstone, Tychonoff’s theorem without the axiom of choice, Fund. Math., to appear.; P.T. Johnstone, Tychonoff’s theorem without the axiom of choice, Fund. Math., to appear. · Zbl 0503.54006 [16] Johnstone, P. T., Factorization and pullback theorems for localic geometric morphisms, (Seminaire de Mathématique Pure, Rapport no. 79 (1979), Université Catholique de Louvain) · Zbl 0454.18007 [17] P.T. Johnstone, The Gleason cover of a topos, II. To appear.; P.T. Johnstone, The Gleason cover of a topos, II. To appear. · Zbl 0445.18005 [18] Kock, A.; Lecouturier, P.; Mikkelsen, C. J., Some topos-theoretic concepts of finiteness, Model Theory and Topoi. Model Theory and Topoi, Springer Lecture Notes in Math., 445, 209-283 (1975) · Zbl 0334.18010 [19] Mioduszewski, J.; Rudolf, L., \(H\)-closed and extremally disconnected Hausdorff spaces, Dissertationes Math., 66 (1969) · Zbl 0204.22404 [20] C.J. Mulvey, The real numbers in a topos. To appear.; C.J. Mulvey, The real numbers in a topos. To appear. [21] Mulvey, C. J., A syntactic construction of the spectrum of a commutative \(C^∗\)-algebra with identity, Tagungsbericht. Tagungsbericht, Oberwolfach Kategorientagung, 73-74 (1977) [22] Pierce, R. S., Modules over commutative regular rings, Memoirs Amer. Math. Soc., 70 (1967) · Zbl 0152.02601 [23] Rainwater, J., A note on projective resolutions, Proc. Amer. Math. Soc., 10, 734-735 (1959) · Zbl 0105.16403 [24] Stone, M. H., Boolean algebras and their applications to topology, Proc. Nat. Acad. Sci. U.S.A., 20, 197-202 (1934) · Zbl 0010.08104 [25] Strauss, D., Extremally disconnected spaces, Proc. Amer. Math. Soc., 18, 305-309 (1967) · Zbl 0147.41302 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.