On closures of discrete sets
- Autori: S. Spadaro
- Anno di pubblicazione: 2021
- Tipologia: Articolo in rivista
- OA Link: http://hdl.handle.net/10447/481005
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 MartÃnez-Ruiz, RamÃrez-Páramo and Romero-Morales, we prove that the cardinal inequality |X|≤g(X)L(X)â‹…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.