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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Points of continuity for semigroup actions


Author: Jimmie D. Lawson
Journal: Trans. Amer. Math. Soc. 284 (1984), 183-202
MSC: Primary 54H15; Secondary 22A15
DOI: https://doi.org/10.1090/S0002-9947-1984-0742420-7
MathSciNet review: 742420
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Abstract: The purpose of this paper is to provide a more unified approach to questions involving the existence of points of joint continuity in separately continuous semigroup actions by deriving a small number of general principles which suffice to deduce previously derived results and generalizations thereof. The first major result gives sufficient conditions for a point to be a point of joint continuity in a general setting of "migrants", a useful symmetric generalization of semigroup actions. Results concerning actions of semigroups with group-like properties follow. In the latter part of the paper the notion of a subordinate point is introduced and joint continuity at subordinate points for various settings is proved. Finally, these results are applied to linear actions on locally convex spaces.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0742420-7
Keywords: Transformation semigroup, separable continuity, point of joint continuity, linear action
Article copyright: © Copyright 1984 American Mathematical Society