Here it is shown that the Kuratowski imbedding of a Riemannian manifold in L∞, exploited in Gromov's proof of the systolic inequality for essential manifolds, admits an approximation by a (1+C)-bi-Lipschitz (onto its image), finite-dimensional imbedding for every C>0. The key tool is the first variation formula thought of as a real statement in first-order logic, in the context of non-standard analysis.
In a related development:
After years of institutionalized denial, research mathematician reveals: .999... can be less than 1, almost everywhere. Read all about it here
Robert Ely's paper examines nonstandard student conceptions
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