C$嵌入、林德洛夫性、切赫完备性

arXiv - MATH - General Topology Pub Date : 2024-04-30 DOI:arxiv-2404.19703

Alan Dow, Klaas Pieter Hart, Jan van Mill, Hans Vermeer

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引用次数: 0

摘要

我们证明了在\v{C}ech-complete 空间的林德尔（Lindel）类中，$C$嵌入的性质是相当良好的。它有一个有用的特征，可以用来证明$C$嵌入空间的乘积和完备预映像也是$C$嵌入的。我们还证明了乘积结果所需要的两个性质，即林德尔性质和 v{C}ech-complete 性质。

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$C$-embedding, Lindelöfness, Čech-completeness

We show that in the class of Lindel\"of \v{C}ech-complete spaces the property of being $C$-embedded is quite well-behaved. It admits a useful characterization that can be used to show that products and perfect preimages of $C$-embedded spaces are again $C$-embedded. We also show that both properties, Lindel\"of and \v{C}ech-complete, are needed in the product result.

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arXiv - MATH - General Topology

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