Geodesic
Initially Structured Categories and Cartesian Closedness
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1361-1377

Voir la notice de l'article provenant de la source Cambridge University Press

In recent papers Horst Herrlich [4; 5] has demonstrated the usefulness of topological categories for applications to a large variety of special structures. A particularly striking result is his characterization of cartesian closedness for topological categories (see [5]). Spaces satisfying a separation axiom usually cannot form a topological category in Herrlich's sense however and some interesting special cases, e.g. Hausdorff C-spaces, remain excluded from his theory despite having many analogous properties. It therefore seems worthwhile to undertake a similar study in a wider setting. To this end we relax one of the axioms for a topological category and show that in the resulting initially structured categories a significant selection of results can still be proved, including the characterization of cartesian closedness. 
Nel, L. D. Initially Structured Categories and Cartesian Closedness. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1361-1377. doi: 10.4153/CJM-1975-139-9
@article{10_4153_CJM_1975_139_9,
     author = {Nel, L. D.},
     title = {Initially {Structured} {Categories} and {Cartesian} {Closedness}},
     journal = {Canadian journal of mathematics},
     pages = {1361--1377},
     year = {1975},
     volume = {27},
     number = {6},
     doi = {10.4153/CJM-1975-139-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-139-9/}
}
TY  - JOUR
AU  - Nel, L. D.
TI  - Initially Structured Categories and Cartesian Closedness
JO  - Canadian journal of mathematics
PY  - 1975
SP  - 1361
EP  - 1377
VL  - 27
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-139-9/
DO  - 10.4153/CJM-1975-139-9
ID  - 10_4153_CJM_1975_139_9
ER  - 
%0 Journal Article
%A Nel, L. D.
%T Initially Structured Categories and Cartesian Closedness
%J Canadian journal of mathematics
%D 1975
%P 1361-1377
%V 27
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1975-139-9/
%R 10.4153/CJM-1975-139-9
%F 10_4153_CJM_1975_139_9

[1] 1. Binz, E. and Keller, H. H., Funktionrdume in der Kategorie der Limesrdume, Ann. Acad. Sci. Fenn. 383 (1966), 1–21. Google Scholar

[2] 2. Herrlich, H. and Strecker, G. E., Category theory (Allyn and Bacon, 1973). Google Scholar

[3] 3. Herrlich, H., Topological functors, Gen. Top. Appl. 4 (1974), 125–142. Google Scholar

[4] 4. Herrlich, H., Topological structures, Math. Centre Tract 52 (1974), 59–122. Google Scholar

[5] 5. Herrlich, H., Cartesian closed topological categories Math. Coll. Univ. Cape Town 9 (1974). 1–16. Google Scholar

[6] 6. Hogbe-Nlend, H., Théorie des homologies et applications, Lecture Notes in Mathematics 213 (Springer 1971). Google Scholar

[7] 7. Kent, D. C., Convergence quotient maps, Fund. Math. 65 (1969), 197–205. Google Scholar

[8] 8. Kent, D. C. and Richardson, G. D., Locally compact convergence spaces (preprint). Google Scholar

[9] 9. Waelbroeck, L., Etude spectrale des algebres completes, Mem. Acad. Royale Belgique, 1960. Google Scholar

Cité par Sources :