Semigroups and Families

  • Ethan Akin
Part of the The University Series in Mathematics book series (USMA)


In this chapter we consider a uniform action φ: T × XX with X compact, and compare the semigroup and family viewpoints. Recall that by Lemma 1.2 any topological action of a uniform monoid on a compact space is a uniform action. The focus of our comparison is the uniform Stone-Čtech compactification of the uniform monoid T. In itself ß u T combines three different phenomena. First T acts uniformly on the compact space ß u T, which is the orbit closure of j u (0) in ß u T. Furthermore using the maps Φ x , we see that this action is the universal compact T action ambit [see (6.18)]. Next ß u T is an Ellis semigroup mapping onto the enveloping semigroup, S φ , by the homomorphism Φ# [see (6.13)]. Finally we recall that ß u T can be regarded as the space of maximal open filters on T as in Theorem 5.2. This connects ß u T with all of the family constructions in Chapters 3 and 4.


Open Filter Invariant Subset Minimal Ideal Minimal Subset Recurrent Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Ethan Akin
    • 1
  1. 1.The City CollegeNew YorkUSA

Personalised recommendations