Search results for " 54D10"

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Urysohn's metrization theorem for higher cardinals

2011

In this paper a generalization of Urysohn's metrization theorem is given for higher cardinals. Namely, it is shown that a topological space with a basis of cardinality at most $|\omega_\mu|$ or smaller is $\omega_\mu$-metrizable if and only if it is $\omega_\mu$-additive and regular, or, equivalently, $\omega_\mu$-additive, zero-dimensional, and T\textsubscript{0}. Furthermore, all such spaces are shown to be embeddable in a suitable generalization of Hilbert's cube.

Mathematics::Logic54F65 54C25 54A25 54D70 54D10 54D20General Topology (math.GN)FOS: MathematicsMathematics::General TopologyAstrophysics::Cosmology and Extragalactic AstrophysicsMathematics - General Topology
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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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