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 ()
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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
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