Multidimensional <inline-formula><tex-math id="M1">$ C^0 $</tex-math></inline-formula> transversality and the shadowing property for Axiom A diffeomorphisms

Petrov and Pilyugin (2015) generalized a notion of $ C^0 $ transversality of Sakai (1995) using smooth curves. Their definition involves only continuous maps from $ {\mathbb R}^n $ to a manifold, which is a purely topological one. They also provided a sufficient condition for the $ C^0 $ transversality in terms of homological nature. In this paper, we prove that such a homological condition of Axiom A diffeomorphisms is sufficient for enjoying the shadowing property. Moreover, it is proved that the $ C^0 $ transversality of Axiom A diffeomorphisms with codimension one basic sets implies the homological condition.