Hostname: page-component-5c6d5d7d68-pkt8n Total loading time: 0 Render date: 2024-08-20T08:50:39.605Z Has data issue: false hasContentIssue false
  • English
  • Français

The category of uniform convergence spaces is cartesian closed

Published online by Cambridge University Press:  17 April 2009

R.S. Lee
R.S. Lee
Affiliation:
Department of Mathematics, Duquesne University, Pittsburgh, Pennsylvania, USA.
Rights & Permissions [Opens in a new window]

Abstract

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.

This paper first assigns specific uniform convergence structures to the products and function spaces of pairs of uniform convergence spaces, and then establishes a bijection between corresponding sets of morphisms which yields cartesian closedness.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 461 - 465
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Cook, C.H. and Fischer, R.H., “Uniform convergence structures”, Math. Ann. 173 (1967), 209–306.CrossRefGoogle Scholar
[2]Gazik, R.J., Kent, D.C., Richardson, G.D., “Regular completions of uniform convergence spaces”, Bull. Austral. Math. Soc. 11 (1974), 413–424.CrossRefGoogle Scholar
[3]Herrlich, Horst, “Cartesian closed topological categories”, Math. Colloq. Univ. Cape Town 9 (1974), 1–16.Google Scholar
[4]Lane, Saunders Mac, Categories for the working mathematician (Graduate Text in Mathematics, 5. Springer-Verlag, New york, Heidelberg, Berlin, 1971).Google Scholar
[5]Nel, L.D., “Cartesian closed topological categories”, Categorical topology, 439–451 (proc. Cof. Mannheim, 1975. Lecture Notes in Mathematics, 540. Springer-Verlag, Berlin, Heidelberg, New York, 1976).Google Scholar
[6]Wyler, Oswald “Convenient categories for topology”, General Topology and Appl. 3 (1973), 225–242.CrossRefGoogle Scholar
[7]Wyler, Oswald, “Filter space monads, regularity, completions”, TOPO 1972 – General topology and its applications, 591–637, (Second Pittsburg International Conference, 1972. Lecture Notes in Mathematics, 378. Springer-Verlag, Berlin, Heidelberg, New York, 1974).Google Scholar