On hereditary and product-stable quotient maps
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 345-352 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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}.
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}.
Classification : 18A20, 18B30, 54A05, 54B30, 54C10
Keywords: hereditary quotient; product-stable quotient; pull\-back-stable quotient; extensional topological hull; CCT hull; topological universe hull; pretopological spaces; pseudotopological spaces
@article{CMUC_1992_33_2_a15,
     author = {Schwarz, Friedhelm and Weck-Schwarz, Sibylle},
     title = {On hereditary and product-stable quotient maps},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {345--352},
     year = {1992},
     volume = {33},
     number = {2},
     mrnumber = {1189666},
     zbl = {0795.18001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a15/}
}
TY  - JOUR
AU  - Schwarz, Friedhelm
AU  - Weck-Schwarz, Sibylle
TI  - On hereditary and product-stable quotient maps
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 345
EP  - 352
VL  - 33
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a15/
LA  - en
ID  - CMUC_1992_33_2_a15
ER  - 
%0 Journal Article
%A Schwarz, Friedhelm
%A Weck-Schwarz, Sibylle
%T On hereditary and product-stable quotient maps
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 345-352
%V 33
%N 2
%U http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a15/
%G en
%F CMUC_1992_33_2_a15
Schwarz, Friedhelm; Weck-Schwarz, Sibylle. On hereditary and product-stable quotient maps. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 2, pp. 345-352. http://geodesic.mathdoc.fr/item/CMUC_1992_33_2_a15/

[Ad 86] Adámek, J.: Classification of concrete categories. Houston J. Math. 12 (1986), 305-326. | MR

[AH 86] Adámek J., Herrlich H.: Cartesian closedness, quasitopoi and topological universes. Comment. Math. Univ. Carolinae 27 (1986), 235-257. | MR

[ARS 91] Adámek J., Reiterman J., Schwarz F.: On universally topological hulls and quasitopos hulls. Houston J. Math. 17 (1991), 375-383. | MR

[Al 85] Alderton I.W.: Cartesian closedness and the MacNeille completion of an initially structured category. Quaestiones Math. 8 (1985), 63-78. | MR | Zbl

[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

[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

[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 | Zbl

[Bo 75] Bourdaud G.: Espaces d'Antoine et semi-espaces d'Antoine. Cahiers Topol. Géom. Différentielle 16 (1975), 107-133. | MR | Zbl

[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 | Zbl

[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

[He 74] Herrlich H.: Cartesian closed topological categories. Math. Colloq. Univ. Cape Town 9 (1974), 1-16. | MR | Zbl

[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 | Zbl

[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 | Zbl

[HN 77] Herrlich H., Nel L.D.: Cartesian closed topological hulls. Proc. Amer. Math. Soc. 62 (1977), 215-222. | MR | Zbl

[Ke 69] Kent D.C.: Convergence quotient maps. Fund. Math. 65 (1969), 197-205. | MR | Zbl

[Mi 68] Michael E.: Bi-quotient maps and cartesian products of quotient maps. Ann. Inst. Fourier Grenoble 18 (1968), 287-302. | MR | Zbl

[Ne 77] Nel L.D.: Cartesian closed coreflective hulls. Quaestiones Math. 2 (1977), 269-283. | MR | Zbl

[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 | Zbl

[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

[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

[We 91] Weck-Schwarz S.: Cartesian closed topological and monotopological hulls: A comparison. Topology Appl. 38 (1991), 263-274. | MR | Zbl

[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 | Zbl