Compact convex sets free of inner points in infinite‐dimensional topological vector spaces

Almudena Campos‐Jiménez and Francisco Javier García‐Pacheco

Mathematische Nachrichten, 2024, vol. 297, issue 5, 1668-1677

Abstract: An inner point of a non‐singleton convex set M$M$ is a point x∈M$x\in M$ satisfying that for all m∈M∖{x}$m\in M\setminus \lbrace x\rbrace$ there exists n∈M∖{m,x}$n\in M\setminus \lbrace m,x\rbrace$ such that x∈(m,n)$x\in (m,n)$. We prove the existence of convex compact subsets free of inner points in the infinite‐dimensional setting. Following our pathway to this result, we come up with other several geometric hits, such as the existence of a non‐convex subset that coincides with its starlike envelope.

Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.202200328

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:297:y:2024:i:5:p:1668-1677

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().