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Approximation of maps from algebraic polyhedra to real algebraic varieties

Approximation of maps from algebraic polyhedra to real algebraic varieties

Given a finite simplicial complex $\mathcal{K}$ in $\mathbb{R}^n$ and a real algebraic variety $Y,$ by a $\mathcal{K}$-regular map $|\mathcal{K}|\rightarrow Y$ we mean a continuous map whose restriction to every simplex in $\mathcal{K}$ is a regular map. A simplified version of our main result says that if $Y$ is a uniformly …