Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



The continuity of Arens' product on the Stone-Čech compactification of semigroups

Author: Nicholas Macri
Journal: Trans. Amer. Math. Soc. 191 (1974), 185-193
MSC: Primary 22A25
MathSciNet review: 0382541
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A discrete semigroup is said to have the compact semigroup property (c.s.p.) [the compact semi-semigroup property (c.s.s.p.)] if the multiplication Arens' product, on its Stone-Čech compactification, is jointly [separately] $ {w^ \ast }$-continuous. We obtain an algebraic characterization of those semigroups which have c.s.p. by characterizing algebraically their almost periodic subsets. We show that a semigroup has c.s.p. if and only if each of its subsets is almost periodic. This characterization is employed to prove that for a cancellation semigroup to have c.s.p., it is necessary and sufficient that each of its countable subsets be almost periodic. We answer in the negative a heretofore open question--is c.s.p. equivalent to c.s.s.p.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22A25

Retrieve articles in all journals with MSC: 22A25

Additional Information

Keywords: Arens' product, joint continuity, separate continuity, Stone-Čech compactification, almost periodic, weakly almost periodic
Article copyright: © Copyright 1974 American Mathematical Society

American Mathematical Society