turkmath.org

In this talk, we give an overview of selection principles theory, one of the most popular branches of mathematics in the last two-three decades.  First, we will discuss the basic ideas and some classical results.  Then we will present star and neighbourhood selection principles and weaker forms of all these principles. One part of the talk will be devoted to applications of statistical and ideal convergence in the theory of selection properties.  Relationships of selection properties with game theory, Ramsey theory, function spaces will be also considered. At the end, some open problems will be posed and directions of further investigations will be suggested.