Pinning Down versus Density

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Juhász, István; Soukup, Lajos; Szentmiklóssy, Zoltán;
(2015)
  • Subject: 03E04, 03E10, 03E35, 54A25, 54A35} | Mathematics - General Topology | Mathematics - Logic

The pinning down number $ {pd}(X)$ of a topological space $X$ is the smallest cardinal $\kappa$ such that for any neighborhood assignment $U:X\to \tau_X$ there is a set $A\in [X]^\kappa$ with $A\cap U(x)\ne\emptyset$ for all $x\in X$. Clearly, c$(X) \le {pd}(X) \le {d}(... View more
  • References (3)

    [1] U. Abraham, M. Magidor, Cardinal arithmetic, Handbook of Set Theory. Vols. 1, 2, 3, 1149-1227, Springer, Dordrecht, 2010.

    [2] Taras Banakh, Alex Ravsky, Verbal covering properties of topological spaces, arXiv:1503.04480

    [3] Saharon Shelah, Cardinal arithmetic for skeptics, American Math Soc Bulletin. New Series 26 (1992) 197-210. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences E-mail address: juhasz@renyi.hu Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences E-mail address: soukup@renyi.hu

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