Bulletin of the
Korean Mathematical Society BKMS

Let $M$ be a generalized homogeneous compact space, and let $Z(M)$ denotes the space of homeomorphisms of $M$ with the $C^0$ topology. In this paper, we show that if the interior of the set of weak stable homeomorphisms on $M$ is not empty then for any open subset $W$ of $Z(M)$ containing only weak stable homeomorphisms the orbital shadowing property is generic in $W$.

Keywords: orbital shadowing property, $\delta$-pseudo-orbit, shadowing property

MSC numbers: Primary 54H20; Secondary 54F99