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Gamma-Sets and the (A, B_∞) Selection Principle

Ballone, Frank A.
http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490350606744796

Abstract Details

2017, Doctor of Philosophy (PhD), Ohio University, Mathematics (Arts and Sciences).
The field of Selection Principles in Mathematics is in some sense the study of diagonalization processes. It has its roots in a few basic selection principles that arose from the study of problems in analysis, dimension theory, topology, and set theory. These "classical" selection principles were formally defined by M. Scheepers in 1996, but they go back to classical works of F. Rothberger, W. Hurewicz, and K. Menger. Since then, new selection principles and new types of covers have been introduced and studied in relation to the classical selection principles. We consider the relationship between gamma-sets, which are spaces satisfying a specific classical selection principle, and a newer selection principle (A, B_∞) that was introduced by B. Tsaban in 2007. First, we survey known results of gamma-sets due to F. Galvin and A.W. Miller and prove which results hold for the (A, B_∞) selection principle. Then, we establish filter characterizations for these selection principles to prove new properties and positively answer a question asked by B. Tsaban. Afterward, we prove several results about a concrete construction of a gamma-set on the Cantor space due to T. Orenshtein and B. Tsaban. Lastly, we revisit our properties to formulate some open questions raised by our work.
Todd Eisworth (Advisor)
Vladimir Uspenskiy (Committee Member)
Sergio Lopez (Committee Member)
Phillip Ehrlich (Committee Member)
75 p.
Mathematics
mathematics; set theory; topology; selection principles; gamma-set; filters; covering properties

Recommended Citations

Citations

  • Ballone, F. A. (2017). Gamma-Sets and the (A, B_∞) Selection Principle [Doctoral dissertation, Ohio University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490350606744796

    APA Style (7th edition)

  • Ballone, Frank. Gamma-Sets and the (A, B_∞) Selection Principle. 2017. Ohio University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490350606744796.

    MLA Style (8th edition)

  • Ballone, Frank. "Gamma-Sets and the (A, B_∞) Selection Principle." Doctoral dissertation, Ohio University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1490350606744796

    Chicago Manual of Style (17th edition)

ohiou1490350606744796
787
© 2017, all rights reserved.
This open access ETD is published by Ohio University and OhioLINK.