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RESEARCH PRODUCT
On the cardinality of almost discretely Lindelof spaces
Santi SpadaroSanti SpadaroAngelo Bellasubject
Discrete mathematicsCardinal inequality Lindelof space Arhangel’skii Theorem elementary submodel left-separated discrete set free sequence.General Mathematics010102 general mathematicsHausdorff spaceGeneral Topology (math.GN)Mathematics::General TopologyMonotonic functionSpace (mathematics)01 natural sciences010101 applied mathematicsMathematics::LogicCardinalityLindelöf spaceFOS: MathematicsSettore MAT/03 - GeometriaContinuum (set theory)0101 mathematicsSubspace topologyAxiomMathematics - General TopologyMathematicsdescription
A space is said to be almost discretely Lindelof if every discrete subset can be covered by a Lindelof subspace. Juhasz et al. (Weakly linearly Lindelof monotonically normal spaces are Lindelof, preprint, arXiv:1610.04506 ) asked whether every almost discretely Lindelof first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under $$2^{<{\mathfrak {c}}}={\mathfrak {c}}$$ (which is a consequence of Martin’s Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhasz et al. (First-countable and almost discretely Lindelof $$T_3$$ spaces have cardinality at most continuum, preprint, arXiv:1612.06651 ). We conclude with a few related results and questions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2016-11-22 |