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Algebraic approximation preserving dimension (1409.6451v1)
Published 23 Sep 2014 in math.AG
Abstract: We prove that each semialgebraic subset of $\Rn$ of positive codimension can be locally approximated of any order by means of an algebraic set of the same dimension. As a consequence of previous results, algebraic approximation preserving dimension holds also for semianalytic sets.
