On closures of discrete sets

2018/11/06 by Spadaro, Santi
#FOS: Mathematics #General Topology (math.GN)

paper · doi:10.48550/arxiv.1811.02264

Abstract

The depth of a topological space X (g(X)) is defined as the supremum of the cardinalities of closures of discrete subsets of X. Solving a problem of Martínez-Ruiz, Ramírez-Páramo and Romero-Morales, we prove that the cardinal inequality |X| ≤ g(X)^{L(X) ⋅ F(X)} holds for every Hausdorff space X, where L(X) is the Lindelöf number of X and F(X) is the supremum of the cardinalities of the free sequences in X.

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