Alan Dow, Klaas Pieter Hart, Jan van Mill, Hans Vermeer
{"title":"C$嵌入、林德洛夫性、切赫完备性","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":"{\"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}","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}
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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