Search results for "Dispersion character"

showing 2 items of 2 documents

Covering by discrete and closed discrete sets.

2008

Say that a cardinal number $\kappa$ is \emph{small} relative to the space $X$ if $\kappa <\Delta(X)$, where $\Delta(X)$ is the least cardinality of a non-empty open set in $X$. We prove that no Baire metric space can be covered by a small number of discrete sets, and give some generalizations. We show a ZFC example of a regular Baire $\sigma$-space and a consistent example of a normal Baire Moore space which can be covered by a small number of discrete sets. We finish with some remarks on linearly ordered spaces.

Open setMathematics::General TopologyBaireBaire measure01 natural sciencesComplete metric spaceDiscrete setFOS: MathematicsProperty of Baire0101 mathematicsDispersion characterMoore spaceMathematicsMathematics - General TopologyDiscrete mathematicsMoore space (topology)σ-space010102 general mathematicsGeneral Topology (math.GN)Baire spaceBaire property010101 applied mathematicsMetric spaceMathematics::Logic54A25 54E52Baire category theoremSettore MAT/03 - GeometriaGeometry and TopologyLOTSsigma-space
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A note on discrete sets

2009

We give several partial positive answers to a question of Juhasz and Szentmiklossy regarding the minimum number of discrete sets required to cover a compact space. We study the relationship between the size of discrete sets, free sequences and their closures with the cardinality of a Hausdorff space, improving known results in the literature.

dispersion characterelementary submodel.Discrete setEberlein compactfree sequence
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