6533b828fe1ef96bd12883df

RESEARCH PRODUCT

Free sequences and the tightness of pseudoradial spaces

Santi Spadaro

subject

Algebra and Number TheoryApplied Mathematics010102 general mathematicsGeneral Topology (math.GN)Hausdorff spaceMathematics::General TopologySpace (mathematics)01 natural sciencesInfimum and supremum010101 applied mathematicsCombinatoricsMathematics::LogicComputational MathematicsCharacter (mathematics)Free sequence tightness Lindelof degree pseudoradialFOS: MathematicsGeometry and TopologySettore MAT/03 - Geometria0101 mathematicsAnalysisMathematics - General TopologyMathematics

description

Let F(X) be the supremum of cardinalities of free sequences in X. We prove that the radial character of every Lindelof Hausdorff almost radial space X and the set-tightness of every Lindelof Hausdorff space are always bounded above by F(X). We then improve a result of Dow, Juhasz, Soukup, Szentmiklossy and Weiss by proving that if X is a Lindelof Hausdorff space, and $$X_\delta $$ denotes the $$G_\delta $$ topology on X then $$t(X_\delta ) \le 2^{t(X)}$$ . Finally, we exploit this to prove that if X is a Lindelof Hausdorff pseudoradial space then $$F(X_\delta ) \le 2^{F(X)}$$ .

10.1007/s13398-020-00861-zhttp://hdl.handle.net/10447/480905