Some Relational and Sequential Results, and a Relational Modification of a False Lemma of Paweł Pasteczka on the Constancy of the Composition of Certain Set-Valued Functions
Zoltán Boros,
Rezső L. Lovas and
Árpád Száz ()
Additional contact information
Zoltán Boros: Department of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
Rezső L. Lovas: Department of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
Árpád Száz: Department of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
Mathematics, 2025, vol. 13, issue 10, 1-43
Abstract:
After establishing some basic facts on binary relations and sequential convergences, we prove a relational modification of a false, but interesting lemma of Paweł Pasteczka on the constancy of the composition of certain set-valued functions [ There is at most one continuous invariant mean , Aequat. Math. 96 (2022), 833–841.]. In particular, we prove that if F is an inclusion-increasing, compact-valued, closed relation of the half line X = [ 0 , + ∞ [ to a sequential convergence space Y = Y ( lim ) , and G is an inclusion-continuous relation of Y to X such that their composition relation Φ = G ∘ F is inclusion-left-continuous, then Φ is a constant relation.
Keywords: relational and sequential convergence spaces; closed and compact sets; closed, closed-valued, inclusion increasing and continuous relations (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/2227-7390/13/10/1594/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/10/1594/ (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:10:p:1594-:d:1654825
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 ().