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Closed Ideals in the Stone-Čech Compactification of a Countable Semigroup and Some Applications to Ergodic Theory and Topological Dynamics

Christopherson, John Cory
http://rave.ohiolink.edu/etdc/view?acc_num=osu1395847452

Abstract Details

2014, Doctor of Philosophy, Ohio State University, Mathematics.
We study the relationship between algebra in the Stone-Čech compactification of a countable semigroup and dynamics. In particular, we establish a correspondence between the closed subsets of the Stone-Čech compactification and certain types of recurrence in compact topological dynamical systems. The notion of recurrence associated to a closed subset A of the Stone-Čech Compactification is most satisfying in the event that A is an ideal (or at least a semigroup). Those notions of recurrence which arise naturally in the study of topological dynamics all correspond to ideals. This general theory is then applied to obtain results pertaining to recurrence in dynamical systems as well as combinatorial results about large sets in countable amenable groups.
Vitaly Bergelson, Dr (Advisor)
124 p.
Mathematics

Recommended Citations

Citations

  • Christopherson, J. C. (2014). Closed Ideals in the Stone-Čech Compactification of a Countable Semigroup and Some Applications to Ergodic Theory and Topological Dynamics [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1395847452

    APA Style (7th edition)

  • Christopherson, John. Closed Ideals in the Stone-Čech Compactification of a Countable Semigroup and Some Applications to Ergodic Theory and Topological Dynamics. 2014. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1395847452.

    MLA Style (8th edition)

  • Christopherson, John. "Closed Ideals in the Stone-Čech Compactification of a Countable Semigroup and Some Applications to Ergodic Theory and Topological Dynamics." Doctoral dissertation, Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1395847452

    Chicago Manual of Style (17th edition)

osu1395847452
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