Topologically subordered rectifiable spaces and compactifications
Topologically subordered rectifiable spaces and compactifications
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DOI：
10.1016/j.topol.2011.10.001
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发表时间：
2011-06
期刊：
影响因子：
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通讯作者：
Fucai Lin
中科院分区：
文献类型：
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作者：
Fucai Lin
一个拓扑空间G称为可求长空间，如果存在一个满射同胚φ：G×G→G×G和一个元素e∈G使得π1 <$φ=π 1，且对每个x∈G有φ（x，x）=（x，e），其中π1：G×G→G是到第一坐标的投影。本文主要讨论了可求长空间的可次序性，证明了若可求长空间是可次序的，则它是可度量化的或完全不连通的P-空间，改进了A. V. Arhangel Schloskienkovich（2009）在[8]中的一个定理.作为应用，我们讨论了GO-空间的Hausdorff紧化的可求正算子，主要讨论了下列命题，以及在什么条件下Φ为真。 此外，我们还考虑了可求长空间的Hausdorff紧化的算子的一些相关问题。
A topological space G is said to be a rectifiable space provided that there are a surjective homeomorphism φ:G×G→G×G and an element e∈G such that π1∘φ=π1and for every x∈G we have φ(x,x)=(x,e), where π1:G×G→G is the projection to the first coordinate. In this paper, we mainly discuss the rectifiable spaces which are suborderable, and show that if a rectifiable space is suborderable then it is metrizable or a totally disconnected P-space, which improves a theorem of A.V. Arhangelʼskiı̌ (2009) in [8]. As an application, we discuss the remainders of the Hausdorff compactifications of GO-spaces which are rectifiable, and we mainly concerned with the following statement, and under what condition Φ it is true. Moreover, we also consider some related matters about the remainders of the Hausdorff compactifications of rectifiable spaces.