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Mathematics
Volume 13
Issue 10
10.3390/math13101594
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

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 †

by
Zoltán Boros
,
Rezso L. Lovas
and
Árpád Száz
*
Department of Mathematics, University of Debrecen, P.O. Box 400, H-4002 Debrecen, Hungary
*
Author to whom correspondence should be addressed.
†
Dedicated to the Memory of our Teacher and Leader Professor Zoltán Daróczy.
Mathematics 2025, 13(10), 1594; https://doi.org/10.3390/math13101594
Submission received: 26 March 2025 / Revised: 6 May 2025 / Accepted: 7 May 2025 / Published: 13 May 2025
(This article belongs to the Collection Topology and Foundations)
Versions Notes

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 atmost one continuous invariant mean, Aequat. Math. 96 (2022), 833–841.]. Inparticular, 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 relational and sequential convergence spaces; closed and compact sets; closed, closed-valued, inclusion increasing and continuous relations

Share and Cite

MDPI and ACS Style

Boros, Z.; Lovas, R.L.; Száz, Á. 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. Mathematics 2025, 13, 1594. https://doi.org/10.3390/math13101594

AMA Style

Boros Z, Lovas RL, Száz Á. 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. Mathematics. 2025; 13(10):1594. https://doi.org/10.3390/math13101594

Chicago/Turabian Style

Boros, Zoltán, Rezso L. Lovas, and Árpád Száz. 2025. "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" Mathematics 13, no. 10: 1594. https://doi.org/10.3390/math13101594

APA Style

Boros, Z., Lovas, R. L., & Száz, Á. (2025). 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. Mathematics, 13(10), 1594. https://doi.org/10.3390/math13101594

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