6533b833fe1ef96bd129c3a2
RESEARCH PRODUCT
On closures of discrete sets
Santi Spadarosubject
CombinatoricsMathematics (miscellaneous)Cardinal invariants Lindelof space Discrete set Elementary submodel CellularityGeneral Topology (math.GN)FOS: MathematicsHausdorff spaceMathematics::General TopologySettore MAT/03 - GeometriaTopological spaceDiscrete setInfimum and supremumMathematics - General TopologyMathematicsdescription
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 Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-11-06 |