# Article

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Keywords:
concentric circle space; weak $G_\delta$-diagonal; point-separating $^\ast$-open cover; cardinal function
Summary:
It is well-known that the concentric circle space has no $G_\delta$-diagonal nor any countable point-separating open cover. In this paper, we reveal two new properties of the concentric circle space, which are the weak versions of $G_\delta$-diagonal and countable point-separating open cover. Then we introduce two new cardinal functions and sharpen some known cardinal inequalities.
References:
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[3] Ginsburg J., Wood G.: A cardinal inequality for topological space involving closed discrete sets. Proc. Amer. Math. Soc. 64 (1977), 357-360. MR 0461407

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