  In this paper we present some applications of A'Campo-L\^e's Theorem and we
study some relations between Zariski's Questions A and B. It is presented some
classes of homeomorphisms that preserve multiplicity and tangent cones of
complex analytic sets. Moreover, we present a class of homeomorphisms that has
the multiplicity as an invariant when we consider right equivalence and this
class contains many known classes of homeomorphisms that preserve tangent
cones. In particular, we present some effective approaches to Zariski's
Question A. We show a version of these results looking at infinity.
Additionally, we present some results related with Nash modification and
Lipschitz Geometry.
