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.
Similar content being viewed by others
References
Brown, R.: Function spaces and product topologies, Quart. J. Math. (2) 15 (1964), 238–250.
Činčura, J.: Closed structures on reflective subcategories of the category of topological spaces, Topology Appl. 37 (1990), 237–247.
Činčura, J.: Cartesian closed coreflective subcategories of the category of topological spaces, Topology Appl. 41 (1991), 205–212.
Činčura, J.: Products in cartesian closed subcategories of the category of topological spaces, Topology Appl. 59 (1994), 195–200.
Eilenberg, S. and Kelly, G. M.: Closed categories, in Proceedings Conference on Categorical Algebra, La Jolla, 1965, Springer, New York, 1996, pp. 421–562.
Greve, G.: Tensor products, coreflective subcategories and α-convergence, Preprint, 1982.
Herrlich, H.: Topologische Reflexionen und Coreflexionen, Lecture Notes in Mathematics 78, Springer, Berlin, 1968.
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.
Herrlich, H.: Cartesian closed topological categories, Math. Colloq. Univ. Cape Town 9 (1974), 1–16.
Herrlich, H. and Hušek, M.: Some open categorical problems in Top, Applied Categorical Structures 1 (1993), 1–19.
Herrlich, H. and Strecker, G. E.: Category Theory, Heldermann, Berlin, 1979.
Kelley, J. L.: General Topology, Van Nostrand, Princeton, NJ, 1955.
Kuratowski, K. and Mostowski, A.: Set Theory, PWN, Warsaw, 1967.
Logar, A. and Rossi, F.: Monoidal closed structures on categories with constant maps, J. Austral. Math. Soc. Ser. A 38 (1985), 175–185.
Mac Lane, S.: Categories for the Working Mathematicians, Springer, New York, 1971.
Nel, L. D.: Initially structured categories and cartesian closedness, Canad. J. Math. 27 (1975), 1361–1377.
Nel, L. D.: Cartesian closed coreflective hulls, Quaestiones Mathematicae 2 (1977), 269–283.
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.
Author information
Authors and Affiliations
Rights 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
Issue Date:
DOI: https://doi.org/10.1023/A:1008667921330