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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
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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

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