Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-25T14:38:21.520Z Has data issue: false hasContentIssue false
  • English
  • Français

The topologies of separate continuity. II

Published online by Cambridge University Press:  24 October 2008

C. J. Knight ,
W. Moran  and
J. S. Pym
C. J. Knight
Affiliation:
University of Sheffield
W. Moran
Affiliation:
University of Sheffield
J. S. Pym
Affiliation:
University of Sheffield
Get access Rights & Permissions [Opens in a new window]

Extract

In (6) we studied a topology T on the product set X × Y of two topological spaces X and Y which was defined by the requirement that each mapping from X × Y which was continuous in each variable separately was also continuous in T; we called (X × Y, T) the tensor product of X and Y, and denoted it by X ⊗ Y. Theorem (3·2) of (6) indicated that X ⊗ Y was rarely completely regular; as complete regularity is of importance in analytic problems, we consider here a ‘completely regular tensor product’ . Roughly speaking, gives a tensor product in the category of completely regular topological spaces. The categorical properties of are discussed in section 5.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 307 - 319
Copyright
Copyright © Cambridge Philosophical Society 1972

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Bourbaki, N.Topologie générate, Chaps. 1 and 2, Actualités Scientifiques et Industrielles 1142 (3rd ed. 1961), Chap. 9, Actualites Scientifiques et Industrielles 1045 (2nd ed. 1958), Hermann, Paris.Google Scholar
(2)Čech, E.Topological spaces. Czech. Academy of Sciences (Prague, 1966).Google Scholar
(3)Freyd, P.Abelian Categories (Harper and Row; New York, 1964).Google Scholar
(4)Gillman, L. and Jerison, M.Rings of continuous Junctions (Van Nostrand; New York, 1960).CrossRefGoogle Scholar
(5)Isbell, J. R.Uniform spaces, Mathematical Surveys 12, American Math. Soc. (1964).CrossRefGoogle Scholar
(6)Knight, C. J., Moran, W. and Pym, J. S.Topologies of separate continuity. Proc. Cambridge Philos. Soc. 68 (1970), 663–671.CrossRefGoogle Scholar
(7)Knowles, J. D.On the existence of non-atomic measures. Mathematika 14 (1967), 62–67.CrossRefGoogle Scholar
(8)Kuratowski, C.Topology I (Academic Press; New York, 1966).Google Scholar
(9)Moran, W.The additivity of measures on completely regular spaces. J. London Math. Soc. 43 (1968), 633–639.CrossRefGoogle Scholar
(10)Moran, W.Separate continuity and supports of measures. J. London Math. Soc. 44 (1969), 320–324.Google Scholar
(11)Moran, W.Measures and mappings on topological spaces. Proc. London Math. Soc. (3), 19 (1969), 493–508.Google Scholar
(12)Morita, K.On the product of a normal space with a metric space. Proc. Japan Acad. 39 (1963), 148–150.Google Scholar
(13)Varadarajan, V. S.Measures on topological spaces. Mat. Sb. 55 (1961), 33–100 (Russian);Google Scholar
Varadarajan, V. S.Measures on topological spaces. Amer. Math. Soc. transl. 48, 141–228.Google Scholar