Bulletin of the
Korean Mathematical Society BKMS

In this paper, $\mathcal{I}$-scattered spaces are introduced, and their characterizations and properties are given. We prove that $(X,\tau)$ is scattered if and only if $(X,\tau,\mathcal{I})$ is $\mathcal{I}$-scattered for any ideal $\mathcal{I}$ on $X$.

Keywords: ideals, scattered spaces, $\mathcal{I}$-scattered spaces, $\ast$-isolated points, $\ast$-derived sets, $\ast$-dense sets, $*$-closed mappings, topological sums

MSC numbers: 03E10, 54A10, 54G12