Sequences and Series in Banach Spaces pp 192-199 | Cite as
An Intermission: Ramsey’s Theorem
Chapter
Abstract
Some notation, special to the present discussion, ought to be introduced. If A and B are subsets of the set N of natural numbers, then we write A < B whenever a < b holds for each a ∈ A and b ∈ B. The collection of finite subsets of A is denoted by ℘ <∞(A) and the collection of infinite subsets of A by ℘ ∞(A). More generally for A,B ⊆ N we denote by ℘ <∞(A,B the colelction { X ∈ ℘ <∞ (N) : A ⊆ X A ∪ B, A < X\ A } and by ℘ ∞ (A,B) the collection { X ∈ ℘ ∞ (N): A ⊆ X ⊆ A ∪ B, A < X\ A }.
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