Milnor-L\^e type fibrations for subanalytic maps

We prove a Milnor-L^e type fibration theorem for a subanalytic map $f: X \to Y$betweensubanalyticsets$X \subset $\mathbb{R}$^m$and$Y \subset $\mathbb{R}$^n$\mathrm{.}Moreover,if$f$extendstoananalyticmap$$\mathbb{R}$^m \to $\mathbb{R}$^n$,wedefinethesingularsetandthediscriminantsetof$f$, in a stratified sense. Then we give Milnor-L^e type fibration theorems for $f$ outside its discriminant, as well as over it. We give examples of each situation approached in this paper.