  In 1994, Sakai introduced the property of $C^0$ transversality for two smooth
curves in a two-dimensional manifold. This property was related to various
shadowing properties of dynamical systems. In this short note, we generalize
this property to arbitrary continuous mappings of topological spaces into
topological manifolds. We prove a sufficient condition for the $C^0$
transversality of two submanifolds of a topological manifold and a necessary
condition of $C^0$ transversality for mappings of metric spaces into
$\mathbb{R}^n$.
