Pacific Journal of Mathematics

Monoidal closed, Cartesian closed and convenient categories of topological spaces.

P. Booth and J. Tillotson

Article information

Source
Pacific J. Math. Volume 88, Number 1 (1980), 35-53.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102779712

Zentralblatt MATH identifier
0436.54008

Zentralblatt MATH identifier
0402.54004

Mathematical Reviews number (MathSciNet)
MR595812

Subjects
Primary: 55U40: Topological categories, foundations of homotopy theory
Secondary: 18B30: Categories of topological spaces and continuous mappings [See also 54-XX] 18D15: Closed categories (closed monoidal and Cartesian closed categories, etc.) 54B10: Product spaces 54C35: Function spaces [See also 46Exx, 58D15]

Citation

Booth, P.; Tillotson, J. Monoidal closed, Cartesian closed and convenient categories of topological spaces. Pacific Journal of Mathematics 88 (1980), no. 1, 35--53. http://projecteuclid.org/euclid.pjm/1102779712.


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References

  • [1] R. Arens and J. Dugundji, Topologies for function spaces, Pacific J. Math., 1 (1951), 5-31.
  • [2] P. Booth, The section problem and the liftingproblem, Math. Z., 121 (1971), 273-287.
  • [3] R. Brown, Ten topologies for XxY,Quart J. Math., (2) 14 (1963), 303-319.
  • [4] R. Brown,Function spaces and product Topologies, Quart J. Math., (2) 15 (1964), 238-250.
  • [5] R. Brown,Elements of Modern Topology, McGraw-Hill, London, 1968.
  • [6] R. Brown,On sequentially proper maps and a sequential compactification, J. London Math. Soc, (2) 7 (1973), 1-8.
  • [7] A. Clark, Quasi-Topology and Compactly Generated Spaces, Mimeographed Notes, Brown University (about 1967), (unpublished).
  • [8] B. Day, A reflection theorem for closed categories, J. Pure and Appl. Algebra, 2 (1972), 1-11.
  • [9] J. Dugundji, Topology, Allyn and Bacon, 1966.
  • [10] S. Eilenberg and G. M. Kelly, ClosedCategories, Proc. Conf. on Categorical Algebra, La Jolla, 1965, Springer-Verlag, Berlin, 1969, 541-552.
  • [11] S. P. Franklin, Spaces in which sequences suffice, Fund. Math., 57 (1965), 107-115.
  • [12] J. Guthrie, On some generalizations of metric spaces, Ph. D. Dissertation, Texas Christian University, 1969.
  • [13] J. Guthrie,A characterization of Q-spaces, General Topology and its Appl., 1 (1971), 105-110.
  • [14] J. L. Kelley, General Topology, Van Nostrand, Princeton, 1955.
  • [15] G. M. Klly, Tensor products in categories, J. Algebra, 2 (1965), 15-37.
  • [16] D. M. Hyman, A category slightly larger than the metric and CW-categories, Michigan Math. J., 15 (1968), 193-214.
  • [17] C. J. Knight, W. Moran and J. S. Pym, The topologies of separate continuityI, Proc. Camb. Phil. Soc, 68 (1970), 663-671.
  • [18] K. Kuratowski, Topology, Vol. I, Academic Press, New York and London, 1966.
  • [19] L. D. Nel, Cartesian closed coreflective hulls, Quaestiones Mathematicae, 2 (1977), 269-283.
  • [20] N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J., 14 (1967), 133-152.
  • [21] J. Tillotson, The convenient category of sequential spaces, Masters thesis, Memorial University of Newfoundland, 1978.
  • [22] R. Vazquez, Espacios funcionles y funtores adjuntos, An. Inst. Math. Univ. Nac. Autnoma Mexico, 6 (1966), 7-46.
  • [23] R. M. Vogt, Convenient categories of topological spaces for homotopy theory, Archiv der Math., 22 (1971), 545-555.
  • [24] P. Wilker, Adjoint product and hornfunctors in general topology, Pacific J. Math., 34 (1970), 269-283.
  • [25] O. Wyler, convenient Categories for topology, General Topology and its Appl., 3 (1973), 225-242.