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

Abstract

In this paper we are interested in parallels to the classical notions of special subsets in R defined in the generalized Cantor and Baire spaces (2 κ and κ κ ). We consider generalizations of well-known classes of special subsets, like Lusin sets, strongly null sets, concentrated sets, perfectly meagre sets, σ-sets, γ-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, T ′ -sets, Marczewski, Silver, Miller and Laver-null sets. We also show some relations between those classes.