{"title":"书中的选择原则和证明","authors":"Boaz Tsaban","doi":"10.4153/s0008439523000905","DOIUrl":null,"url":null,"abstract":"<p>I provide simplified proofs for each of the following fundamental theorems regarding selection principles: </p><ol><li><p><span>(1)</span> The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of continuous functions on a space is actually preserved by Borel images of that space.</p></li><li><p><span>(2)</span> The Scheepers Diagram Last Theorem, due to Peng, completing all provable implications in the diagram.</p></li><li><p><span>(3)</span> The Menger Game Theorem, due to Telgársky, determining when Bob has a winning strategy in the game version of Menger’s covering property.</p></li><li><p><span>(4)</span> A lower bound on the additivity of Rothberger’s covering property, due to Carlson.</p></li></ol><p></p><p>The simplified proofs lead to several new results.</p>","PeriodicalId":501184,"journal":{"name":"Canadian Mathematical Bulletin","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Selection principles and proofs from the Book\",\"authors\":\"Boaz Tsaban\",\"doi\":\"10.4153/s0008439523000905\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>I provide simplified proofs for each of the following fundamental theorems regarding selection principles: </p><ol><li><p><span>(1)</span> The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of continuous functions on a space is actually preserved by Borel images of that space.</p></li><li><p><span>(2)</span> The Scheepers Diagram Last Theorem, due to Peng, completing all provable implications in the diagram.</p></li><li><p><span>(3)</span> The Menger Game Theorem, due to Telgársky, determining when Bob has a winning strategy in the game version of Menger’s covering property.</p></li><li><p><span>(4)</span> A lower bound on the additivity of Rothberger’s covering property, due to Carlson.</p></li></ol><p></p><p>The simplified proofs lead to several new results.</p>\",\"PeriodicalId\":501184,\"journal\":{\"name\":\"Canadian Mathematical Bulletin\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-11-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Mathematical Bulletin\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008439523000905\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Mathematical Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4153/s0008439523000905","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我为以下有关选择原则的基本定理逐一提供了简化证明：(1)准正收敛定理，作者和兹德姆斯基提出，断言空间上连续函数空间的某一重要性质实际上被该空间的伯勒尔图像所保留。 (2)谢珀斯图最后定理，彭提出，完成了图中所有可证明的含义。(3) Telgársky 提出的门格尔博弈定理（Menger Game Theorem），确定了在门格尔覆盖性质的博弈版本中，鲍勃何时有获胜策略。 (4) 卡尔森提出的罗斯伯格覆盖性质可加性的下限。
I provide simplified proofs for each of the following fundamental theorems regarding selection principles:
(1) The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of continuous functions on a space is actually preserved by Borel images of that space.
(2) The Scheepers Diagram Last Theorem, due to Peng, completing all provable implications in the diagram.
(3) The Menger Game Theorem, due to Telgársky, determining when Bob has a winning strategy in the game version of Menger’s covering property.
(4) A lower bound on the additivity of Rothberger’s covering property, due to Carlson.
The simplified proofs lead to several new results.
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