On spaces of Conradian group orderings
On spaces of Conradian group orderings
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论康拉德群序空间
DOI：
10.1515/jgt.2009.053
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
C. Rivas
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文献类型：
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作者：
C. Rivas
摘要我们对仅允许有限多个C-序的C-可序群进行了分类。我们证明了：如果一个C-可序群有无限多个C-序，那么它有无数个C-序，并且这些C-序都不是孤立在C-序空间中的。我们仔细研究了Baumgrag-Solitar群B(1，2)的情形，证明了它有四个C-序，每个C-序都是双不变的，但它的左序空间与Cantor集是同胚的。
Abstract We classify C-orderable groups admitting only finitely many C-orderings. We show that if a C-orderable group has infinitely many C-orderings, then it has uncountably many C-orderings, and none of these is isolated in the space of C-orderings. We carefully study the case of the Baumslag–Solitar group B(1, 2) and show that it has four C-orderings, each of which is bi-invariant, but that its space of left-orderings is homeomorphic to the Cantor set.