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Approximate homomorphisms on lattices

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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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Acknowledgements

We thank the referee for his/her valuable remarks and the suggestion of extending Corollary 10 to the case of general linearly ordered sets.

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Correspondence to Tomasz Kochanek.

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The research of the third-named author is a part of the Iterative functional equations and real analysis program (Institute of Mathematics, University of Silesia, Katowice, Poland).

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Badora, R., Kochanek, T. & Przebieracz, B. Approximate homomorphisms on lattices. Arch. Math. 111, 177–186 (2018). https://doi.org/10.1007/s00013-018-1182-0

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  • DOI: https://doi.org/10.1007/s00013-018-1182-0

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