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.
On closures of discrete sets
S. Spadaro
2018-01-01
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.File in questo prodotto:
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