Points of continuity for semigroup actions
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. © 1984 American Mathematical Society.
Publication Source (Journal or Book title)
Transactions of the American Mathematical Society
Lawson, J. (1984). Points of continuity for semigroup actions. Transactions of the American Mathematical Society, 284 (1), 183-202. https://doi.org/10.1090/S0002-9947-1984-0742420-7