A student of Adi Jarden and mine attempts at generalizing results on selection principles from the Baire space $\omega^\omega$ to the higher Baire space $\kappa^\kappa$ ($\kappa$ uncountable), and similarly for the higher Cantor space $2^\kappa$, with the initial segment topology, as defined here and here. This leads (see linked questions) to many elementary questions whose answers are likely to be known.

We would appreciate references to surveys of this type of "higher descriptive set theory" and its basic results. In particular, it would be nice if these deal with results like Cantor-Bendixon Theorem, and combinatorial cardinals of the (higher) continuum.