Remainders of rectifiable spaces
Remainders of rectifiable spaces
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DOI：
10.1016/j.topol.2009.08.028
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发表时间：
2010-03
影响因子：
0.6
通讯作者：
A. Arhangel'skii;M. Choban
中科院分区：
文献类型：
--
作者：
A. Arhangel'skii;M. Choban
我们证明一个二分定理：对于任意可整流空间 G 的任何 Hausdorff 紧致 bG，余数 bG∖G 要么是伪紧，要么是 Lindelöf。该定理概括了 A.V. 早期获得的关于拓扑群的类似定理。 Arhangel'skii (2008) [6]，但可整流空间的证明比拓扑群的情况要复杂得多。由此可见，如果可整流空间 G 的余数是仿紧或 Dieudonné 完备的，则余数是 Lindelöf 并且 G 是 p 空间。我们还提供了一个例子，表明二分定理并不适用于所有副拓扑群。获得了一些其他结果，并提出了一些悬而未决的问题。
We prove a Dichotomy Theorem: for any Hausdorff compactification bG of an arbitrary rectifiable space G, the remainder bG∖G is either pseudocompact or Lindelöf. This theorem generalizes a similar theorem on topological groups obtained earlier in A.V. Arhangel'skii (2008) [6], but the proof for rectifiable spaces is considerably more involved than in the case of topological groups. It follows that if a remainder of a rectifiable space G is paracompact or Dieudonné complete, then the remainder is Lindelöf and that G is a p-space. We also present an example showing that the Dichotomy Theorem does not extend to all paratopological groups. Some other results are obtained, and some open questions are formulated.