Properties of ideals on the generalized Cantor spaces

Abstract

AbstractWe define a class of productiveσ-ideals of subsets of the Cantor space 2ω and observe that both σ-ideals of meagre sets and of null sets are in this class. From every productive σ-ideal we produce a σ-ideal of subsets of the generalized Cantor space 2κ. In particular, starting from meagre sets and null sets in 2ω we obtain meagre sets and null sets in 2ω, respectively. Then we investigate additivity, covering number, uniformity and cofinality of . For example, we show thatOur results generalizes those from [5].