Let (X, 0) be the germ of either a subanalytic set X subset of Rn$X \subset {\mathbb {R}}<^>n$ or a complex analytic space X subset of Cn$X \subset {\mathbb {C}}<^>n$, and let f:(X,0)->(Kk,0)$f: (X,0) \rightarrow ({\mathbb {K}}<^>k, 0)$ be a K${\mathbb {K}}$-analytic map-germ, with K=R${\mathbb {K}}={\mathbb {R}}$ or C${\mathbb {C}}$, respectively. When k=1$k=1$, there is a well-known topological locally trivial fibration associated with f, called the Milnor-Le fibration of f, which is one of the main pillars in the study of singularities of maps and spaces. However, when k>1$k>1$ that is not always the case. In this paper, we give conditions which guarantee that the image of f is well-defined as a set-germ, and that f admits a Milnor-Le fibration. We also give conditions for f to have the Thom property. Finally, we apply our results to mixed function-germs of type fg over bar :(X,0)->(C,0)$f \bar{g}: (X,0) \rightarrow ({\mathbb {C}},0)$ on a complex analytic surface X subset of Cn$X \subset {\mathbb {C}}<^>n$ with arbitrary singularity.