Skip to main content
Log in

Tensor Products in Categories of Topological Spaces

  • Published:
Applied Categorical Structures Aims and scope Submit manuscript

Abstract

In this paper symmetric monoidal closed structures on coreflective subcategories of the category of (Hausdorff) topological spaces are studied. We describe all such structures on the category of (Hausdorff) pseudoradial spaces and some of its subcategories and give an example of a coreflective subcategory of the category of Hausdorff topological spaces admitting a proper class of symmetric monoidal closed structures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Brown, R.: Function spaces and product topologies, Quart. J. Math. (2) 15 (1964), 238–250.

    Google Scholar 

  2. Činčura, J.: Closed structures on reflective subcategories of the category of topological spaces, Topology Appl. 37 (1990), 237–247.

    Article  Google Scholar 

  3. Činčura, J.: Cartesian closed coreflective subcategories of the category of topological spaces, Topology Appl. 41 (1991), 205–212.

    Article  Google Scholar 

  4. Činčura, J.: Products in cartesian closed subcategories of the category of topological spaces, Topology Appl. 59 (1994), 195–200.

    Article  Google Scholar 

  5. Eilenberg, S. and Kelly, G. M.: Closed categories, in Proceedings Conference on Categorical Algebra, La Jolla, 1965, Springer, New York, 1996, pp. 421–562.

    Google Scholar 

  6. Greve, G.: Tensor products, coreflective subcategories and α-convergence, Preprint, 1982.

  7. Herrlich, H.: Topologische Reflexionen und Coreflexionen, Lecture Notes in Mathematics 78, Springer, Berlin, 1968.

    Google Scholar 

  8. Herrlich, H.: Categorical topology 1971–1981, in General Topology and Its Relations to Modern Analysis and Algebra V, Proceedings Fifth Prague Topological Symposium 1981, Heldermann, Berlin, 1982, pp. 279–383.

    Google Scholar 

  9. Herrlich, H.: Cartesian closed topological categories, Math. Colloq. Univ. Cape Town 9 (1974), 1–16.

    Google Scholar 

  10. Herrlich, H. and Hušek, M.: Some open categorical problems in Top, Applied Categorical Structures 1 (1993), 1–19.

    Google Scholar 

  11. Herrlich, H. and Strecker, G. E.: Category Theory, Heldermann, Berlin, 1979.

    Google Scholar 

  12. Kelley, J. L.: General Topology, Van Nostrand, Princeton, NJ, 1955.

    Google Scholar 

  13. Kuratowski, K. and Mostowski, A.: Set Theory, PWN, Warsaw, 1967.

    Google Scholar 

  14. Logar, A. and Rossi, F.: Monoidal closed structures on categories with constant maps, J. Austral. Math. Soc. Ser. A 38 (1985), 175–185.

    Google Scholar 

  15. Mac Lane, S.: Categories for the Working Mathematicians, Springer, New York, 1971.

    Google Scholar 

  16. Nel, L. D.: Initially structured categories and cartesian closedness, Canad. J. Math. 27 (1975), 1361–1377.

    Google Scholar 

  17. Nel, L. D.: Cartesian closed coreflective hulls, Quaestiones Mathematicae 2 (1977), 269–283.

    Google Scholar 

  18. Nyikos, P. J.: Convergence in toppology, in M. Hušek and J. van Mill (eds), Recent Progress in General Topology, Elsevier, Amsterdam, 1992, pp. 538–570.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Činčura, J. Tensor Products in Categories of Topological Spaces. Applied Categorical Structures 5, 111–122 (1997). https://doi.org/10.1023/A:1008667921330

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1008667921330

Navigation