The theory of subanalytic sets is an excellent tool in various analytic-geometric contexts; see, for example, Bierstone and Milman [1]. Regrettably, certain “nice” sets—like { (x, x) : x > 0 } for positive irrational r, and { (x, e−1/x) : x > 0 }—are not subanalytic (at the origin) in R. Here we make available an extension of the category of subanalytic sets that has these sets among its object...