Function algebras and the lattice of compactifications

Author:

Mendivil Franklin

Abstract

We provide some conditions as to when K ( X ) K ( Y ) K(X) \cong K(Y) for two locally compact spaces X X and Y Y (where K ( X ) K(X) is the lattice of all Hausdorff compactifications of X X ). More specifically, we prove that K ( X ) K ( Y ) K(X) \cong K(Y) if and only if C ( X ) / C 0 ( X ) C ( Y ) / C 0 ( Y ) C^*(X)/C_0(X) \cong C^*(Y)/C_0(Y) . Using this result, we prove several extensions to the case where K ( X ) K(X) is embedded as a sub-lattice of K ( Y ) K(Y) and to where X X and Y Y are not locally compact. One major contribution is in the use of function algebra techniques. The use of these techniques makes the extensions simple and clean and brings new tools to the subject.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. Continua as remainders in compact extensions;Aarts, J. M.;Nieuw Arch. Wisk. (3),1967

2. Lecture Notes in Pure and Applied Mathematics, Vol. 23;Chandler, Richard E.,1976

3. Lattices and compactifications. I, II, III;Firby, P. A.;Proc. London Math. Soc. (3),1973

4. Graduate Texts in Mathematics, No. 43;Gillman, Leonard,1976

5. A note on compactifications;Magill, Kenneth D., Jr.;Math. Z.,1966

Cited by 9 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Domains of commutative C*-subalgebras;Mathematical Structures in Computer Science;2019-03-21

2. Structure of abelian parts of C * -algebras and its preservers;Acta Scientiarum Mathematicarum;2018

3. Symmetries in Exact Bohrification;Springer Proceedings in Mathematics & Statistics;2018

4. Foundations of Quantum Theory;Fundamental Theories of Physics;2017

5. Domains of Commutative C-Subalgebras;2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science;2015-07

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3