On the definability of Menger spaces which are not /sigma-compact
classification
🧮 math.GN
keywords
mengerspacessigma-compactmetrizablecech-completeco-analyticcompletelyconsistent
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Hurewicz proved completely metrizable Menger spaces are /sigma-compact. We extend this to Cech-complete Menger spaces and consistently to projective Menger metrizable spaces. On the other hand, it is consistent that there is a co-analytic Menger space that is not /sigma-compact.
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