On mysterious subsets of the real line and their applicable topological-algebraic counterparts.

‎‎‎We will present new topological and set-theoretic results with some applications (both in topology and functional analysis) concerning -spaces and -spaces and their connections with objects on the real line such as -sets and -sets.
We discuss also recent results about Baire -resolvable spaces which are -spaces.
A number of open problems in this area will be provided.