On $\mathcal{I}$-scattered spaces
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 667-680
https://doi.org/10.4134/BKMS.2014.51.3.667
Published online May 31, 2014
Zhaowen Li and Shizhan Lu
Guangxi University for Nationalities, Guangxi University for Nationalities
Abstract : 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
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