N - 的前象的自同胚

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-03-19 DOI:10.1016/j.topol.2025.109348

Alan Dow

{"title":"N - <s:1>的前象的自同胚","authors":"Alan Dow","doi":"10.1016/j.topol.2025.109348","DOIUrl":null,"url":null,"abstract":"<div><div>In the study of the Stone-Čech remainder of the real line a detailed study of the Stone-Čech remainder of the space <span><math><mi>N</mi><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, which we denote as <span><math><mi>M</mi></math></span>, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to <span><math><mi>M</mi></math></span>. It is known that an autohomeomorphism of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> induces an autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. We prove that it is consistent with there being non-trivial autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> that those induced by autohomeomorphisms of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> are trivial.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"368 ","pages":"Article 109348"},"PeriodicalIF":0.6000,"publicationDate":"2025-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Autohomeomorphisms of pre-images of N⁎\",\"authors\":\"Alan Dow\",\"doi\":\"10.1016/j.topol.2025.109348\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In the study of the Stone-Čech remainder of the real line a detailed study of the Stone-Čech remainder of the space <span><math><mi>N</mi><mo>×</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>, which we denote as <span><math><mi>M</mi></math></span>, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to <span><math><mi>M</mi></math></span>. It is known that an autohomeomorphism of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> induces an autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>. We prove that it is consistent with there being non-trivial autohomeomorphism of <span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> that those induced by autohomeomorphisms of <span><math><msup><mrow><mi>M</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> are trivial.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"368 \",\"pages\":\"Article 109348\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2025-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0166864125001464\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0166864125001464","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

在实线的Stone-Čech余量的研究中，经常使用对空间nx[0,1]的Stone-Čech余量的详细研究，我们将其表示为M。当然实线可以被两个同胚于M的闭集所覆盖，已知M的自同胚可以诱导出N的自同胚。证明了由M的自同胚诱导的自同胚是平凡的，与N的非平凡自同胚的存在是一致的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Autohomeomorphisms of pre-images of N⁎

In the study of the Stone-Čech remainder of the real line a detailed study of the Stone-Čech remainder of the space

N \times [0, 1]

, which we denote as

M

, has often been utilized. Of course the real line can be covered by two closed sets that are each homeomorphic to

M

. It is known that an autohomeomorphism of

M^{⁎}

induces an autohomeomorphism of

N^{⁎}

. We prove that it is consistent with there being non-trivial autohomeomorphism of

N^{⁎}

that those induced by autohomeomorphisms of

M^{⁎}

are trivial.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.