| This dissertation introduces weighted jets, establishes weighted versions of Verdier regularity condition (w), Thom-Verdier regularity condition ;Let ;Let ;First we establish the weighted version of Verdier's Isotopy Theorem, which gives topological equisingularity along each connected component of each stratum of a stratification ;Then we introduce an interpolation lemma which constructs a map with given order of derivatives, and apply it to get the equivalence between ;We also consider the V-sufficiency, SV-sufficiency and R-sufficiency, corresponding to variety equivalence, strong variety equivalence and right equivalence, respectively. In addition, the equivalence between the respective sufficiency and Kuo's condition is established by showing the relation between Lojasiewicz condition and Kuo's condition. |
