Unified characterization of exponential objects in TOP, PRTOP and PARATOP
Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 48 (2007) no. 1, p. 70-80
@article{CTGDC_2007__48_1_70_0,
     author = {Mynard, Frederic},
     title = {Unified characterization of exponential objects in TOP, PRTOP and PARATOP},
     journal = {Cahiers de Topologie et G\'eom\'etrie Diff\'erentielle Cat\'egoriques},
     publisher = {Dunod \'editeur, publi\'e avec le concours du CNRS},
     volume = {48},
     number = {1},
     year = {2007},
     pages = {70-80},
     zbl = {1136.54006},
     mrnumber = {2317296},
     language = {en},
     url = {http://www.numdam.org/item/CTGDC_2007__48_1_70_0}
}
Mynard, Frederic. Unified characterization of exponential objects in TOP, PRTOP and PARATOP. Cahiers de Topologie et Géométrie Différentielle Catégoriques, Volume 48 (2007) no. 1, pp. 70-80. http://www.numdam.org/item/CTGDC_2007__48_1_70_0/

1. J. Adȥmek, H. Herrlich, and E. Strecker, Abstract and concrete categories, John Wiley and Sons, Inc., 1990. | MR 1051419 | Zbl 0695.18001

2. G. Bourdaud, Espaces d'Antoine et semi-espaces d'Antoine, Cahiers de Topologies et Géométrie Différentielle 16 (1975), 107-133. | Numdam | MR 394529 | Zbl 0315.54005

3. G. Bourdaud, Some cartesian closed topological categories of convergence spaces, Categorical Topology, Springer-Verlag, 1975, Lecture Notes in Math 540, pp. 93 -108. | MR 493924 | Zbl 0332.54004

4. C. H. Cook and H. R. Fischer, On equicontinuity and continuous convergence, Math. Ann. 159 (1965), 94-104. | MR 179752 | Zbl 0129.38001

5. S. Dolecki, Convergence-theoretic methods in quotient quest, Topology Appl. 73 (1996), 1-21. | MR 1413721 | Zbl 0862.54001

6. S. Dolecki and F. Mynard, Convergence-theoretic mechanisms behind product theorems, Topology Appl. 104 (2000), 67-99. | MR 1780899 | Zbl 0953.54002

7. S. Dolecki and F. Mynard, Hyperconvergences., Appl. Gen. Top. 4 (2003), no. 2, 391-419. | MR 2071211 | Zbl 1068.54010

8. G. Gierz, K. H. Hofmann, K. Keimel, J. Lawson, M. Mislove, and D. Scott, A compedium of continuous lattices, Springer-Verlag, Berlin, 1980. | MR 614752 | Zbl 0452.06001

9. R. Heckmann, A non-topologlcal view of dcpos as convergence spaces., Theoret. Comput. Sci. 305 (2003), no. 1-3, 159-186. | MR 2013570 | Zbl 1053.54018

10. H. Herrlich, Cartesian closed topological categories, Math. Coll. Univ. CapeTown 9 (1974), 1-16. | MR 460414 | Zbl 0318.18011

11. F. Jordan, I. Labuda, and F. Mynard, Finite products of filters that are compact relative to a class of filters, preprint (2005). | MR 2398508 | Zbl 1155.54002

12. E. Lowen-Colebunders and G. Sonck, Exponential objects and cartesian closedness in the construct PRTOP, Appl. Cat. Struct. 1 (1993), 345-360. | MR 1268508 | Zbl 0796.54019

13. E. Michael, A quintuple quotient quest, Gen. Topology Appl. 2 (1972), 91-138. | MR 309045 | Zbl 0238.54009

14. F. Mynard, Coreflectively modified continuous duality applied to classical product theorems, Appl. Gen. Top. 2 (2) (2002), 119-154. | MR 1890032 | Zbl 1007.54008

15. F. Mynard, Coreflectively modified duality, Rocky Mountain J. of Math. 34 (2004), no. 2, 733-758. | MR 2072804 | Zbl 1052.54016

16. F. Mynard, D-compactoid relations and product theorems, (2004), preprint.

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. | MR 785032 | Zbl 0553.18004