Remainders in compactifications and generalized metrizability properties
Remainders in compactifications and generalized metrizability properties
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DOI：
10.1016/j.topol.2004.10.015
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发表时间：
2005-05
影响因子：
0.6
通讯作者：
A. Arhangel'skii
中科院分区：
文献类型：
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作者：
A. Arhangel'skii
Tychonoff空间X何时具有Hausdorff紧化且余数属于给定的一类空间？应用Henriksen和Isbell的经典定理和一些定理，得到了拓扑空间和群的余数上的新结果，这些定理涉及到一个新的完备型性质。特别是，建立了拓扑群具有可度量余数或拟紧p余数的一些强必要条件（该群本身是一个拟紧p空间（定理4.8））。由此得出，如果非局部紧拓扑群G在无穷远处是可度量的，则G是Lindelöf p空间，并且G的苏斯林数是可数的（推论4.10）。这就解决了[M]中的题10.28。Hušek， J. van Mill（编），一般拓扑学的最新进展，第2卷，北荷兰，2002年，第1-57页。
When does a Tychonoff space X have a Hausdorff compactification with the remainder belonging to a given class of spaces? A classical theorem of Henriksen and Isbell and certain theorems, involving a new completeness type property introduced below, are applied to obtain new results on remainders of topological spaces and groups. In particular, some strong necessary conditions for a topological group to have a metrizable remainder, or a paracompact p-remainder, are established (the group itself turns out to be a paracompact p-space (Theorem 4.8)). It follows that if a non-locally compact topological group G is metrizable at infinity, then G is a Lindelöf p-space, and the Souslin number of G is countable (Corollary 4.10). This solves Problem 10.28 from [M. Hušek, J. van Mill (Eds.), Recent Progress in General Topology, vol. 2, North-Holland, 2002, pp. 1–57].