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In this paper, we are interested in parallels to the classical notions ofspecial subsets in $\R$ defined in the generalized Cantor and Baire spaces($2^\kappa$ and $\kappa^\kappa$). We consider generalizations of the well-knownclasses of special subsets, like Lusin sets, strongly null sets, concentratedsets, perfectly meagre sets, $\sigma$-sets, $\gamma$-sets, sets with Menger,Rothberger or Hurewicz property, but also of some less-know classes like$X$-small sets, meagre additive sets, Ramsey null sets, Marczewski, Silver,Miller and Laver-null sets. We notice that many classical theorems regardingthese classes can be relatively easy generalized to higher cardinals althoughsometimes with some additional assumptions. This paper serves as a catalogue ofsuch results along with some other generalizations and open problems.

Special subsets of the generalized Cantor space $2^\kappa$ and generalized Baire space $\kappa^\kappa$