非奇异变换群上的拓扑

IF 0.3 Q4 LOGIC Journal of Logic and Analysis Pub Date : 2022-01-01 DOI:10.4115/jla.2022.14.4
François LE MAÎTRE
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引用次数: 0

摘要

本文证明了关于非奇异变换群上的波兰群拓扑的几个结果。首先证明了具有有限测度支持的实直线的保测度变换群不携带波兰群拓扑。然后我们在一个标准Borel空间上刻画了Borel $\sigma$ -有限测度$\lambda$,对于该空间,$\lambda$ -保持变换群具有自动连续性。我们最后证明了所有非奇异变换群上的自然波兰拓扑实际上是它唯一的波兰群拓扑。
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Polish topologies on groups of non-singular transformations
In this paper, we prove several results concerning Polish group topologies on groups of non-singular transformation. We first prove that the group of measure-preserving transformations of the real line whose support has finite measure carries no Polish group topology. We then characterize the Borel $\sigma$-finite measures $\lambda$ on a standard Borel space for which the group of $\lambda$-preserving transformations has the automatic continuity property. We finally show that the natural Polish topology on the group of all non-singular transformations is actually its only Polish group topology.
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
2
审稿时长
35 weeks
期刊介绍: "Journal of Logic and Analysis" publishes papers of high quality involving interaction between ideas or techniques from mathematical logic and other areas of mathematics (especially - but not limited to - pure and applied analysis). The journal welcomes papers in nonstandard analysis and related areas of applied model theory; papers involving interplay between mathematics and logic (including foundational aspects of such interplay); mathematical papers using or developing analytical methods having connections to any area of mathematical logic. "Journal of Logic and Analysis" is intended to be a natural home for papers with an essential interaction between mathematical logic and other areas of mathematics, rather than for papers purely in logic or analysis.
期刊最新文献
Fractals and the monadic second order theory of one successor A computational study of a class of recursive inequalities Generalized effective completeness for continuous logic Polish topologies on groups of non-singular transformations Compactness of $\omega^\lambda$ for $\lambda$ singular
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