Approximate homomorphisms on lattices
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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.
KeywordsUlam stability Distributive lattice Lattice homomorphism
Mathematics Subject Classification06B23 06D99 39B82
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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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