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Some Ramsey type theorems for normed and quasinormed spaces

C. HensonNigel KaltonN. PeckIgnác TereščákPavol Zlatoš — 1997

Studia Mathematica

We prove that every bounded, uniformly separated sequence in a normed space contains a “uniformly independent” subsequence (see definition); the constants involved do not depend on the sequence or the space. The finite version of this result is true for all quasinormed spaces. We give a counterexample to the infinite version in L p [ 0 , 1 ] for each 0 < p < 1. Some consequences for nonstandard topological vector spaces are derived.

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