Unified characterization of exponential objects in TOP, PRTOP and PARATOP

Frederic Mynard

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2007)

  • Volume: 48, Issue: 1, page 70-80
  • ISSN: 1245-530X

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Mynard, Frederic. "Unified characterization of exponential objects in TOP, PRTOP and PARATOP." Cahiers de Topologie et Géométrie Différentielle Catégoriques 48.1 (2007): 70-80. <http://eudml.org/doc/91714>.

@article{Mynard2007,
author = {Mynard, Frederic},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {exponential objects; function spaces; cartesian closedness; convergence spaces},
language = {eng},
number = {1},
pages = {70-80},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Unified characterization of exponential objects in TOP, PRTOP and PARATOP},
url = {http://eudml.org/doc/91714},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Mynard, Frederic
TI - Unified characterization of exponential objects in TOP, PRTOP and PARATOP
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2007
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 48
IS - 1
SP - 70
EP - 80
LA - eng
KW - exponential objects; function spaces; cartesian closedness; convergence spaces
UR - http://eudml.org/doc/91714
ER -

References

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  3. 3. G. Bourdaud, Some cartesian closed topological categories of convergence spaces, Categorical Topology, Springer-Verlag, 1975, Lecture Notes in Math 540, pp. 93 -108. Zbl0332.54004MR493924
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  7. 7. S. Dolecki and F. Mynard, Hyperconvergences., Appl. Gen. Top. 4 (2003), no. 2, 391-419. Zbl1068.54010MR2071211
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  9. 9. R. Heckmann, A non-topologlcal view of dcpos as convergence spaces., Theoret. Comput. Sci. 305 (2003), no. 1-3, 159-186. Zbl1053.54018MR2013570
  10. 10. H. Herrlich, Cartesian closed topological categories, Math. Coll. Univ. CapeTown 9 (1974), 1-16. Zbl0318.18011MR460414
  11. 11. F. Jordan, I. Labuda, and F. Mynard, Finite products of filters that are compact relative to a class of filters, preprint (2005). Zbl1155.54002MR2398508
  12. 12. E. Lowen-Colebunders and G. Sonck, Exponential objects and cartesian closedness in the construct PRTOP, Appl. Cat. Struct. 1 (1993), 345-360. Zbl0796.54019MR1268508
  13. 13. E. Michael, A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91-138. Zbl0238.54009MR309045
  14. 14. F. Mynard, Coreflectively modified continuous duality applied to classical product theorems, Appl. Gen. Top. 2 (2) (2002), 119-154. Zbl1007.54008MR1890032
  15. 15. F. Mynard, Coreflectively modified duality, Rocky Mountain J. of Math. 34 (2004), no. 2, 733-758. Zbl1052.54016MR2072804
  16. 16. F. Mynard, D-compactoid relations and product theorems, (2004), preprint. 
  17. 17. F. Schwarz, Product compatible reflectors and exponentiality, Proceedings of the International Conference Held at the University of Toledo (Berlin) (Bentley & Al., ed.), Heldermann, 1983, pp. 505-522. Zbl0553.18004MR785032

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