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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.

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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