Regularity and positional games

Abstract

1.Introduction. Suppose X is a set, 𝒞 a collection of sets (usually subsets of X), and N is cardinal number. Following the terminology of Rado [1], we say 𝒞 is N-regular in X if,for any partition of X into N parts, some part has as a subset a member of 𝒞. if 𝒞 is n-regular in X for each integer n, we say 𝒞 is regular in X.