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.
|Numero di pagine||5|
|Stato di pubblicazione||Published - 2019|
All Science Journal Classification (ASJC) codes
- Mathematics (miscellaneous)