Approximation by zero-free continuous maps

2025/08/08 by Alexander J. Izzo, Izzo, Alexander J.
Mathematics · #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2508.05931

Abstract

We prove that if E a subset of an n-dimensional manifold, then every continuous Rⁿ-valued map on E that is zero-free on the interior of E can be approximated in the fine topology, and hence, in particular, in the uniform topology, by a continuous Rⁿ-valued map that is zero-free on all of E.

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