Alan Dow, Klaas Pieter Hart, Jan van Mill, Hans Vermeer
{"title":"$C$-embedding, Lindelöfness, Čech-completeness","authors":"Alan Dow, Klaas Pieter Hart, Jan van Mill, Hans Vermeer","doi":"arxiv-2404.19703","DOIUrl":null,"url":null,"abstract":"We show that in the class of Lindel\\\"of \\v{C}ech-complete spaces the property\nof being $C$-embedded is quite well-behaved. It admits a useful\ncharacterization that can be used to show that products and perfect preimages\nof $C$-embedded spaces are again $C$-embedded. We also show that both\nproperties, Lindel\\\"of and \\v{C}ech-complete, are needed in the product result.","PeriodicalId":501314,"journal":{"name":"arXiv - MATH - General Topology","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - General Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2404.19703","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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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