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Embedding topological spaces into Hausdorff κ-bounded spaces
Topology and its Applications ( IF 0.6 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.topol.2020.107277
Taras Banakh , Serhii Bardyla , Alex Ravsky

Abstract Let κ be an infinite cardinal. A topological space X is κ-bounded if the closure of any subset of cardinality ≤κ in X is compact. We discuss the problem of embeddability of topological spaces into Hausdorff (Urysohn, regular) κ-bounded spaces, and present a canonical construction of such an embedding. Also we construct a (consistent) example of a sequentially compact separable regular space that cannot be embedded into a Hausdorff ω-bounded space.

中文翻译:

将拓扑空间嵌入 Hausdorff κ 有界空间

摘要 令 κ 是一个无穷大的基数。如果 X 中基数≤κ 的任何子集的闭包是紧的,则拓扑空间 X 是 κ 有界的。我们讨论了拓扑空间嵌入 Hausdorff (Urysohn,regular) κ 有界空间的问题,并提出了这种嵌入的规范构造。此外,我们构造了一个(一致的)顺序紧凑的可分正则空间的示例,该空间不能嵌入到 Hausdorff ω 有界空间中。
更新日期:2020-07-01
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