  This paper deals with Hensel minimal structures on non-trivially valued
fields $K$. The main aim is to establish the following two properties of closed
0-definable subsets $A$ in the affine spaces $K^{n}$. Every such subset $A$ is
the zero locus of a continuous 0-definable function $f:K^{n} \to K$, and there
exists a 0-definable retraction $r: K^{n} \to A$. While the former property is
a non-Archimedean counterpart of the one from o-minimal geometry, the former
does not hold in real geometry in general. The proofs make use of a
model-theoretic compactness argument and ubiquity of clopen sets in
non-Archimedean geometry.
