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Displaying similar documents to “Lech inequalities for deformations of singularities defined by power products of degree 2.”

On finite-dimensional maps and other maps with "small" fibers

Yaki Sternfeld (1995)

Fundamenta Mathematicae

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We prove that if f is a k-dimensional map on a compact metrizable space X then there exists a σ-compact (k-1)-dimensional subset A of X such that f|X∖A is 1-dimensional. Equivalently, there exists a map g of X in I k such that dim(f × g)=1. These are extensions of theorems by Toruńczyk and Pasynkov obtained under the additional assumption that f(X) is finite-dimensional.  These results are then extended to maps with fibers restricted to some classes of spaces other than the class of k-dimensional...