Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-28T07:20:17.709Z Has data issue: false hasContentIssue false
  • English
  • Français

Initially Structured Categories and Cartesian Closedness

Published online by Cambridge University Press:  20 November 2018

L. D. Nel
L. D. Nel*
Affiliation:
Carleton University, Ottawa, Ontario
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 6 , 01 December 1975 , pp. 1361 - 1377
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Binz, E. and Keller, H. H., Funktionrdume in der Kategorie der Limesrdume, Ann. Acad. Sci. Fenn. 383 (1966), 1–21.Google Scholar
2. Herrlich, H. and Strecker, G. E., Category theory (Allyn and Bacon, 1973).Google Scholar
3. Herrlich, H., Topological functors, Gen. Top. Appl. 4 (1974), 125–142.Google Scholar
4. Herrlich, H., Topological structures, Math. Centre Tract 52 (1974), 59–122.Google Scholar
5. Herrlich, H., Cartesian closed topological categories Math. Coll. Univ. Cape Town 9 (1974). 1–16.Google Scholar
6. Hogbe-Nlend, H., Théorie des homologies et applications, Lecture Notes in Mathematics 213 (Springer 1971).Google Scholar
7. Kent, D. C., Convergence quotient maps, Fund. Math. 65 (1969), 197–205.Google Scholar
8. Kent, D. C. and Richardson, G. D., Locally compact convergence spaces (preprint).Google Scholar
9. Waelbroeck, L., Etude spectrale des algebres completes, Mem. Acad. Royale Belgique, 1960.Google Scholar