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Keywords:
hereditary quotient; product-stable quotient; pull\-back-stable quotient; extensional topological hull; CCT hull; topological universe hull; pretopological spaces; pseudotopological spaces
hereditary quotient; product-stable quotient; pull\-back-stable quotient; extensional topological hull; CCT hull; topological universe hull; pretopological spaces; pseudotopological spaces
Summary:
It is shown that the quotient maps of a monotopological construct {\bf A} which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of {\bf A}.
References:
[Ad 86] Adámek, J.: Classification of concrete categories. Houston J. Math. 12 (1986), 305-326. MR 0869114
[AH 86] Adámek J., Herrlich H.: Cartesian closedness, quasitopoi and topological universes. Comment. Math. Univ. Carolinae 27 (1986), 235-257. MR 0857544
[ARS 91] Adámek J., Reiterman J., Schwarz F.: On universally topological hulls and quasitopos hulls. Houston J. Math. 17 (1991), 375-383. MR 1126601
[Al 85] Alderton I.W.: Cartesian closedness and the MacNeille completion of an initially structured category. Quaestiones Math. 8 (1985), 63-78. MR 0821433 | Zbl 0586.18006
[Ar 63] Arhangel'skiĭ A.: Some types of factor mappings, and the relations between classes of topological spaces. Soviet Math. Dokl. 4 (1963), 1726-1729 Russian original Dokl. Akad. Nauk SSSR 153 (1963), 743-746. MR 0158362
[Ar 66] Arhangel'skiĭ A.: Mappings and spaces. Russian Math. Surveys 21 (1966), 115-162 Russian original Uspehi Mat. Nauk 21 (1966),133-184. MR 0227950
[BHL 91] Bentley H.L., Herrlich H., Lowen R.: Improving constructions in topology. Category Theory at Work H. Herrlich and H.-E. Porst (eds.) Heldermann Berlin (1991), 3-20. MR 1147915 | Zbl 0753.18002
[Bo 75] Bourdaud G.: Espaces d'Antoine et semi-espaces d'Antoine. Cahiers Topol. Géom. Différentielle 16 (1975), 107-133. MR 0394529 | Zbl 0315.54005
[DK 70] Day B.J., Kelly G.M.: On topological quotient maps preserved by pullbacks or products. Proc. Camb. Phil. Soc. 67 (1970), 553-558. MR 0254817 | Zbl 0191.20801
[Ha 66] Hájek O.: Notes on quotient maps. Comment. Math. Univ. Carolinae 7 (1966), 319-323 Correction Comment. Math. Univ. Carolinae 8 (1967), 171. MR 0202118
[He 74] Herrlich H.: Cartesian closed topological categories. Math. Colloq. Univ. Cape Town 9 (1974), 1-16. MR 0460414 | Zbl 0318.18011
[He 88a] Herrlich H.: Hereditary topological constructs. General Topology and Its Relations to Modern Analysis and Algebra VI (Proc. Prague 1986), Z. Frolík (ed.) Heldermann Berlin (1988), 249-262. MR 0952611 | Zbl 0662.18003
[He 88b] Herrlich H.: On the representability of partial morphisms in Top and in related constructs. Categorical Algebra and Its Applications (Proc. Louvain-la-Neuve 1987), F. Bourceux (ed.), Lecture Notes Math. 1348 Springer Berlin et al. (1988), 143-153. MR 0975967 | Zbl 0662.18004
[HN 77] Herrlich H., Nel L.D.: Cartesian closed topological hulls. Proc. Amer. Math. Soc. 62 (1977), 215-222. MR 0476831 | Zbl 0361.18006
[Ke 69] Kent D.C.: Convergence quotient maps. Fund. Math. 65 (1969), 197-205. MR 0250258 | Zbl 0179.51002
[Mi 68] Michael E.: Bi-quotient maps and cartesian products of quotient maps. Ann. Inst. Fourier Grenoble 18 (1968), 287-302. MR 0244964 | Zbl 0175.19704
[Ne 77] Nel L.D.: Cartesian closed coreflective hulls. Quaestiones Math. 2 (1977), 269-283. MR 0480687 | Zbl 0366.18008
[RT 91] Reiterman J., Tholen W.: Effective descent maps of topological spaces. York University Report 91-33 (1991).
[Sc 86] Schwarz F.: Hereditary topological categories and topological universes. Quaestiones Math. 10 (1986), 197-216. MR 0871020 | Zbl 0621.54007
[Sc 89] Schwarz F.: Description of the topological universe hull. Categorical Methods in Computer Science with Aspects from Topology (Proc. Berlin 1988), E. Ehrig et al. (eds.), Lecture Notes Computer Science 393 Springer Berlin et al. (1989), 325-332. MR 1048372
[Sc 90] Schwarz F.: Extensionable topological hulls and topological universe hulls inside the category of pseudotopological spaces. Comment. Math. Univ. Carolinae 31 (1990), 123-127. MR 1056179
[We 91] Weck-Schwarz S.: Cartesian closed topological and monotopological hulls: A comparison. Topology Appl. 38 (1991), 263-274. MR 1098906 | Zbl 0733.18007
[Wy 76] Wyler O.: Are there topoi in topology?. Categorical Topology (Proc. Mannheim 1975), E. Binz and H. Herrlich (eds.), Lecture Notes Math. 540 Springer Berlin et al. (1976), 699-719. MR 0458346 | Zbl 0354.54001
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