Thompson Rivers University

Science Seminar Series: xi-Weakly Convergence

Dr. Khazhakanush Varazdat Navoyan of the department of mathematics at TRU presents xi-Weakly Convergence as part of the Science Seminar Series.

What the talk is about

A Schreier set is a subset of natural numbers with a size not larger than its least element. For a fixed n, let M_n denote the collection of all those Schreier sets whose greatest element is n. It turns out that there is a connection between Schreier sets and Fibonacci numbers. In particular, the nth Fibonacci number is equal to the length of M_n.

In the list of Schreier families, the collection of all Schreier sets is the first one. Schreier families, because of being enumerated through ordinals, give a rise to the quantified convergence definition, placed between weak and strong convergences. Well-observed (classical) convergences in weak and strong (norm) topologies prove to be particular cases of the quantified convergence in the language of ordinals. The work introduced in this talk is an example of the set theory concepts application to functional analysis.