Selection Priniciples in Mathematics (an overview)
The theory of selection principles deals with the possibility of obtaining mathematically significant objects by selecting elements from sequences of sets. The studied properties mainly include covering properties, measure- and category-theoretic properties, and local properties in topological spaces, especially functions spaces. Often, the characterization of a mathematical property using selectionprinciple is a nontrivial task leading to new insights on the characterized property.
I will give an overview of this theory and, if time permits, present some resent results obtained jointly with Boaz Tsaban and Lyubomyr Zdomskyy.