Extensions and Applications of Locally Solid Convergence Structures

Saeed Hashemi Sababe ()
Additional contact information
Saeed Hashemi Sababe: R&D Section, Data Premier Analytics, Edmonton, AB T8H-0L6, Canada

Mathematics, 2025, vol. 13, issue 7, 1-77

Abstract: Locally solid convergence structures provide a unifying framework for both topological and non-topological convergences in vector lattice theory. In this paper, we explore various extensions and applications of locally solid convergence structures. We characterize unbounded locally solid convergences in different spaces, establish connections with bornological convergences, and investigate their applications in functional analysis. Additionally, we generalize these structures to non-Archimedean vector lattices and compare them with traditional topological frameworks. Finally, we develop applications in fixed point theory and operator spaces. Our results contribute to a deeper understanding of the interplay between different types of convergence structures in mathematical analysis.

Keywords: vector lattice; convergence structure; unbounded convergence; bornology; function spaces; fixed points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/7/1173/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/7/1173/ (text/html)

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:gam:jmathe:v:13:y:2025:i:7:p:1173-:d:1626791

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().