A Remark on a Theorem of Erdos
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subsetinfinitetheoremcardinalityerdoseverysamealgebraic
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A theorem of Erdos asserts that every infinite subset of Euclidean n-space R^n has a subset of the same cardinality having no repeated distances. This theorem is generalized here as follows: If (R^n,E) is an algebraic hypergraph that does not have an infinite, complete subset, then every infinite subset of it has an independent subset of the same cardinality.
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