A Banach space C(K) reading the dimension of K

Głodkowski, Damian

doi:10.1016/j.jfa.2023.109986

Journal of Functional Analysis

2023

DOI: 10.1016/j.jfa.2023.109986

|View full text |Cite

A Banach space C(K) reading the dimension of K

Damian Głodkowski

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Countably tight dual ball with a nonseparable measure

Koszmider,

Silber

2024

Journal of London Math Soc

View full text Add to dashboard Cite

We construct a compact Hausdorff space such that the space of Radon probability measures on considered with the topology (induced from the space of continuous functions ) is countably tight that is a generalization of sequentiality (i.e., if a measure is in the closure of a set , there is a countable such that is in the closure of ) but carries a Radon probability measure that has uncountable Maharam type (i.e., is nonseparable). The construction uses (necessarily) an additional set‐theoretic assumption (the principle) as it was already known, by a result of Fremlin, that it is consistent that such spaces do not exist. This should be compared with the result of Plebanek and Sobota who showed that countable tightness of implies that all Radon measures on have countable type. So, our example shows that the tightness of and of can be different as well as may have Corson property (C), while fails to have it answering a question of Pol. Our construction is also a relevant example in the general context of injective tensor products of Banach spaces complementing recent results of Avilés, Martínez‐Cervantes, Rodríguez, and Rueda Zoca.

show abstract

Countably tight dual ball with a nonseparable measure

Koszmider,

Silber

2024

Journal of London Math Soc

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

A Banach space C(K) reading the dimension of K

Cited by 1 publication

References 26 publications

Countably tight dual ball with a nonseparable measure

Countably tight dual ball with a nonseparable measure

Contact Info

Product

Resources

About