On hereditary and product-stable quotient maps

Friedhelm Schwarz; Sibylle Weck-Schwarz

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 2, page 345-352
  • ISSN: 0010-2628

Abstract

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It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.

How to cite

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Schwarz, Friedhelm, and Weck-Schwarz, Sibylle. "On hereditary and product-stable quotient maps." Commentationes Mathematicae Universitatis Carolinae 33.2 (1992): 345-352. <http://eudml.org/doc/247395>.

@article{Schwarz1992,
abstract = {It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.},
author = {Schwarz, Friedhelm, Weck-Schwarz, Sibylle},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {hereditary quotient; product-stable quotient; pullback-stable quotient; extensional topological hull; CCT hull; topological universe hull; pretopological spaces; pseudotopological spaces; quotient maps; topological spaces; pretopological spaces; monotopological construct},
language = {eng},
number = {2},
pages = {345-352},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On hereditary and product-stable quotient maps},
url = {http://eudml.org/doc/247395},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Schwarz, Friedhelm
AU - Weck-Schwarz, Sibylle
TI - On hereditary and product-stable quotient maps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 2
SP - 345
EP - 352
AB - It is shown that the quotient maps of a monotopological construct A which are preserved by pullbacks along embeddings, projections, or arbitrary morphisms, can be characterized by being quotient maps in appropriate extensions of A.
LA - eng
KW - hereditary quotient; product-stable quotient; pullback-stable quotient; extensional topological hull; CCT hull; topological universe hull; pretopological spaces; pseudotopological spaces; quotient maps; topological spaces; pretopological spaces; monotopological construct
UR - http://eudml.org/doc/247395
ER -

References

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  1. Adámek, J., Classification of concrete categories, Houston J. Math. 12 (1986), 305-326. (1986) MR0869114
  2. Adámek J., Herrlich H., Cartesian closedness, quasitopoi and topological universes, Comment. Math. Univ. Carolinae 27 (1986), 235-257. (1986) MR0857544
  3. Adámek J., Reiterman J., Schwarz F., On universally topological hulls and quasitopos hulls, Houston J. Math. 17 (1991), 375-383. (1991) MR1126601
  4. Alderton I.W., Cartesian closedness and the MacNeille completion of an initially structured category, Quaestiones Math. 8 (1985), 63-78. (1985) Zbl0586.18006MR0821433
  5. 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. (1963) MR0158362
  6. Arhangel'skiĭ A., Mappings and spaces, Russian Math. Surveys 21 (1966), 115-162 Russian original Uspehi Mat. Nauk 21 (1966),133-184. (1966) MR0227950
  7. 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. (1991) Zbl0753.18002MR1147915
  8. Bourdaud G., Espaces d'Antoine et semi-espaces d'Antoine, Cahiers Topol. Géom. Différentielle 16 (1975), 107-133. (1975) Zbl0315.54005MR0394529
  9. Day B.J., Kelly G.M., On topological quotient maps preserved by pullbacks or products, Proc. Camb. Phil. Soc. 67 (1970), 553-558. (1970) Zbl0191.20801MR0254817
  10. Hájek O., Notes on quotient maps, Comment. Math. Univ. Carolinae 7 (1966), 319-323 Correction Comment. Math. Univ. Carolinae 8 (1967), 171. (1967) MR0202118
  11. Herrlich H., Cartesian closed topological categories, Math. Colloq. Univ. Cape Town 9 (1974), 1-16. (1974) Zbl0318.18011MR0460414
  12. 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. (1988) Zbl0662.18003MR0952611
  13. 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. (1988) Zbl0662.18004MR0975967
  14. Herrlich H., Nel L.D., Cartesian closed topological hulls, Proc. Amer. Math. Soc. 62 (1977), 215-222. (1977) Zbl0361.18006MR0476831
  15. Kent D.C., Convergence quotient maps, Fund. Math. 65 (1969), 197-205. (1969) Zbl0179.51002MR0250258
  16. Michael E., Bi-quotient maps and cartesian products of quotient maps, Ann. Inst. Fourier Grenoble 18 (1968), 287-302. (1968) Zbl0175.19704MR0244964
  17. Nel L.D., Cartesian closed coreflective hulls, Quaestiones Math. 2 (1977), 269-283. (1977) Zbl0366.18008MR0480687
  18. Reiterman J., Tholen W., Effective descent maps of topological spaces, York University Report 91-33 (1991). (1991) 
  19. Schwarz F., Hereditary topological categories and topological universes, Quaestiones Math. 10 (1986), 197-216. (1986) Zbl0621.54007MR0871020
  20. 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. (1989) MR1048372
  21. Schwarz F., Extensionable topological hulls and topological universe hulls inside the category of pseudotopological spaces, Comment. Math. Univ. Carolinae 31 (1990), 123-127. (1990) MR1056179
  22. Weck-Schwarz S., Cartesian closed topological and monotopological hulls: A comparison, Topology Appl. 38 (1991), 263-274. (1991) Zbl0733.18007MR1098906
  23. 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. (1976) Zbl0354.54001MR0458346

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