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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
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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.

Information

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

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References

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