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The topologies of separate continuity. I

Published online by Cambridge University Press:  24 October 2008

C. J. Knight ,
W. Moran  and
J. S. Pym
C. J. Knight
Affiliation:
Department of Pure Mathematics, The University, Sheffield, 10
W. Moran
Affiliation:
Department of Pure Mathematics, The University, Sheffield, 10
J. S. Pym
Affiliation:
Department of Pure Mathematics, The University, Sheffield, 10
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Extract

A function f( , ) of two variables is said to be separately continuous if for each fixed y and each fixed x, the functions f(, y) and f(x,) are continuous functions of one variable. Separately continuous functions seem to be playing a larger rôle in analysis than formerly. In (1) there is an account of the theory of semigroups in which the multiplication is separately continuous, and in (9) various analytic theorems are obtained by the study of separately continuous functions f(s, t), where t ranges over a set T, and s ranges over a set of functions on T.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 3 , November 1970 , pp. 663 - 671
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

REFERENCES

(1)Berglund, J. F. and Hofmann, K. H.Compact semitopological semigroups and weakly almost periodic functions. Lecture notes in mathematics 42 (Berlin; Springer-Verlag, 1967).CrossRefGoogle Scholar
(2)Bourbaki, N.Théorie des ensembles, Ch. m, §11, para. 1. Actualités Scientifiques et Industrielles 1243 (Hermann; Paris, 1956).Google Scholar
(3)Brown, R.Elements of modern topology (London; McGraw Hill, 1968).Google Scholar
(4)Ĉech, E.Topological spaces (New York; Interscience, 1966).Google Scholar
(5)Cohen, D. E.Spaces with weak topology. Quart J. Math. Oxford Ser. 5 (1954), 77–80.CrossRefGoogle Scholar
(6)Gelbaum, B. R. and Olmstead, J. M. H.Counterexamples in analysis (San Francisco; Holden-Day, 1964).Google Scholar
(7)Gillman, L. and Jerison, M.Rings of continuous functions (Princeton; Van Nostrand, 1960).CrossRefGoogle Scholar
(8)Isbell, J. R.Uniform spaces (Mathematical Surveys, 12, American Mathematical Society, 1964).CrossRefGoogle Scholar
(9)Ptak, V.An extension theorem for separately continuous functions and its applications to functional analysis. Czechoslovak Math. J. 14 (89) (1964), 562–581.CrossRefGoogle Scholar