关于o自由序列与紧性

IF 0.5 4区 数学 Q3 MATHEMATICS
Nathan Carlson
{"title":"关于o自由序列与紧性","authors":"Nathan Carlson","doi":"10.1016/j.topol.2025.109631","DOIUrl":null,"url":null,"abstract":"<div><div>We use the notion of an <em>o</em>-free sequence to give new bounds for the cardinality of Hausdorff spaces and regular spaces. There are several implications for compacta. One is that if <em>X</em> is a compactum then <span><math><mi>w</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>≤</mo><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span>, where <span><math><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the <em>o</em>-tightness introduced by Tkachenko. Another is that <span><math><mo>|</mo><mi>X</mi><mo>|</mo><mo>≤</mo><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo><mi>w</mi><msub><mrow><mi>ψ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> if <em>X</em> is a compactum. This is shown to be a strict improvement of Arhangel'skiĭ's bound <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>ψ</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span>. Finally, we show <span><math><mo>|</mo><mi>X</mi><mo>|</mo><mo>≤</mo><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo><mi>π</mi><mi>χ</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> if <em>X</em> is a homogeneous compactum. We note <span><math><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo><mi>π</mi><mi>χ</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup><mo>≤</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> for such spaces, where <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> is de la Vega's bound for the cardinality of homogeneous compacta.</div></div>","PeriodicalId":51201,"journal":{"name":"Topology and its Applications","volume":"377 ","pages":"Article 109631"},"PeriodicalIF":0.5000,"publicationDate":"2025-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On o-free sequences and compacta\",\"authors\":\"Nathan Carlson\",\"doi\":\"10.1016/j.topol.2025.109631\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We use the notion of an <em>o</em>-free sequence to give new bounds for the cardinality of Hausdorff spaces and regular spaces. There are several implications for compacta. One is that if <em>X</em> is a compactum then <span><math><mi>w</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>≤</mo><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span>, where <span><math><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is the <em>o</em>-tightness introduced by Tkachenko. Another is that <span><math><mo>|</mo><mi>X</mi><mo>|</mo><mo>≤</mo><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo><mi>w</mi><msub><mrow><mi>ψ</mi></mrow><mrow><mi>c</mi></mrow></msub><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> if <em>X</em> is a compactum. This is shown to be a strict improvement of Arhangel'skiĭ's bound <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>ψ</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span>. Finally, we show <span><math><mo>|</mo><mi>X</mi><mo>|</mo><mo>≤</mo><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo><mi>π</mi><mi>χ</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> if <em>X</em> is a homogeneous compactum. We note <span><math><mi>h</mi><mi>L</mi><msup><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mrow><mi>o</mi><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo><mi>π</mi><mi>χ</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup><mo>≤</mo><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> for such spaces, where <span><math><msup><mrow><mn>2</mn></mrow><mrow><mi>t</mi><mo>(</mo><mi>X</mi><mo>)</mo></mrow></msup></math></span> is de la Vega's bound for the cardinality of homogeneous compacta.</div></div>\",\"PeriodicalId\":51201,\"journal\":{\"name\":\"Topology and its Applications\",\"volume\":\"377 \",\"pages\":\"Article 109631\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2025-10-06\",\"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/S0166864125004298\",\"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/S0166864125004298","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

我们利用无0序列的概念给出了Hausdorff空间和正则空间的基数的新边界。compact有几个含义。一是如果X是紧致,则w(X)≤hL(X)ot(X),其中ot(X)为Tkachenko引入的o紧性。另一个是|X|≤hL(X)ot(X)wψc(X),如果X是紧致的。这被证明是Arhangel'ski 's界2ψ(X)的严格改进。最后,我们证明了如果X是齐次紧致,|X|≤hL(X)ot(X)πχ(X)。我们注意到hL(X)ot(X)πχ(X)≤2t(X),其中2t(X)是齐次紧的基数的de la Vega界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On o-free sequences and compacta
We use the notion of an o-free sequence to give new bounds for the cardinality of Hausdorff spaces and regular spaces. There are several implications for compacta. One is that if X is a compactum then w(X)hL(X)ot(X), where ot(X) is the o-tightness introduced by Tkachenko. Another is that |X|hL(X)ot(X)wψc(X) if X is a compactum. This is shown to be a strict improvement of Arhangel'skiĭ's bound 2ψ(X). Finally, we show |X|hL(X)ot(X)πχ(X) if X is a homogeneous compactum. We note hL(X)ot(X)πχ(X)2t(X) for such spaces, where 2t(X) is de la Vega's bound for the cardinality of homogeneous compacta.
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
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信