0000000000640420

AUTHOR

Leandro F. Aurichi

showing 2 related works from this author

Cardinal estimates involving the weak Lindelöf game

2021

AbstractWe show that if X is a first-countable Urysohn space where player II has a winning strategy in the game $$G^{\omega _1}_1({\mathcal {O}}, {\mathcal {O}}_D)$$ G 1 ω 1 ( O , O D ) (the weak Lindelöf game of length $$\omega _1$$ ω 1 ) then X has cardinality at most continuum. This may be considered a partial answer to an old question of Bell, Ginsburg and Woods. It is also the best result of this kind since there are Hausdorff first-countable spaces of arbitrarily large cardinality where player II has a winning strategy even in the weak Lindelöf game of countable length. We also tackle the problem of finding a bound on the cardinality of a first-countable space where player II has a wi…

Algebra and Number TheoryCardinal invariants Cardinality bounds First-countable Lindelöf Topological game Weakly LindelöfApplied MathematicsFirst-countable spaceHausdorff spaceESPAÇOS TOPOLÓGICOSUrysohn and completely Hausdorff spacesCombinatoricsComputational MathematicsTopological gameCardinalityCompact spaceCountable setSettore MAT/03 - GeometriaGeometry and TopologyContinuum (set theory)AnalysisMathematicsRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
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Selective versions of chain condition-type properties

2015

We study selective and game-theoretic versions of properties like the ccc, weak Lindel\"ofness and separability, giving various characterizations of them and exploring connections between these properties and some classical cardinal invariants of the continuum.

Pure mathematicsRothberger spaceGeneral MathematicsMathematics::General TopologyType (model theory)01 natural sciencesChain (algebraic topology)FOS: Mathematicstopological games0101 mathematicsMathematics - General TopologyMathematicsDiscrete mathematicsContinuum (topology)010102 general mathematicsGeneral Topology (math.GN)TEORIA DOS JOGOSMathematics - Logic16. Peace & justice010101 applied mathematicsMathematics::LogicPrimary: 54A25 03E17 91A44 Secondary: 54D35 54D10selection principlescardinal inequalitiesLogic (math.LO)Chain conditionsActa Mathematica Hungarica
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