Regularity and Positional Games
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 , 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.
KeywordsChoice Function Finite Subset Arithmetic Progression Cardinal Number Commutative Semigroup
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