Approximate homomorphisms on lattices
Roman Badora, Tomasz Kochanek, Barbara Przebieracz
TL;DR
This paper investigates the stability of approximate lattice homomorphisms, providing new results on their behavior under general error functions and neighborhood systems, with implications for approximately monotone functions.
Contribution
It introduces novel stability results for approximate lattice homomorphisms using general error estimates and neighborhood systems, extending Ulam-type stability theory.
Findings
Stability results for approximate lattice homomorphisms with general error functions
Stability of approximate join homomorphisms via lattice neighborhoods
Corollary on stability of approximately monotone functions
Abstract
We prove two results concerning an Ulam-type stability problem for homomorphisms between lattices. One of them involves estimates by quite general error functions; the other deals with approximate (join) homomorphisms in terms of certain systems of lattice neighborhoods. As a corollary, we obtain a stability result for approximately monotone functions.
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