门格尔猜想的可定义版本

摘要：

门格尔的猜想，门格尔空间是/σ-紧的是假的;这是正确的解析子空间的波兰空间和不可判定的更复杂的可定义子空间的波兰空间。对于不可度量化的空间，解析Menger空间是/σ-紧的，但余解析空间的Menger连续像不一定是。一般的共解析情形仍然是开放的，但许多特殊情形是不可判定的，特别是Menger拓扑群。我们还证明了如果存在Michael空间，则乘积Lindelof Cech-完备空间是σ-紧的.我们也给出了许多特征的适当的K-Lusin空间。我们的方法包括公理的协分析确定性，非度量化的描述集合论，和Arhangel'skii的工作广义度量空间。

英文摘要：

Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces are /sigma-compact, but Menger continuous images of co-analytic spaces need not be. The general co-analytic case is still open, but many special cases are undecidable, in particular, Menger topological groups. We also prove that if there is a Michael space, then productively Lindelof Cech-complete spaces are /sigma-compact. We also give numerous characterizations of proper K-Lusin spaces. Our methods include the Axiom of Co-analytic Determinacy, non-metrizable descriptive set theory, and Arhangel'skii's work on generalized metric spaces.

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