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Keywords:
concentric circle space; weak $G_\delta $-diagonal; point-separating $^\ast $-open cover; cardinal function
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:
[1] Burke D.K., Hodel R.: The number of compact subsets of a topological space. Proc. Amer. Math. Soc. 58 (1976), 363-368. MR 0418014 | Zbl 0335.54005
[2] Engelking R.: General Topology. Warszawa, 1977. MR 0500780 | Zbl 0684.54001
[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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