Abstract
We will prove a kind of stability result for homomorphisms from locally compact to completely regular topological universal algebras with respect to the compact-open topology on the space of all continuous functions between them. More precisely, given such algebras A and B and two additional set-valued mappings controlling the continuity of (partial) functions g from A to B and the range of the sets g(a) for individual elements \({a \in A}\) , every “controlled” partial function behaving almost like a homomorphism on a sufficiently big compact subset of A is arbitrarily close to a continuous homomorphism A → B on a compact set given in advance. We will give some counterexamples, showing the necessity of the assumptions, and discuss some special cases, among them a purely algebraic problem of extendability of finite partial functions to homomorphisms.
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Presented by M. Ploŝĉica.
Research supported by the VEGA grant 1/0588/09.
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Zlatoš, P. Stability of homomorphisms in the compact-open topology. Algebra Univers. 64, 203–212 (2010). https://doi.org/10.1007/s00012-010-0099-7
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DOI: https://doi.org/10.1007/s00012-010-0099-7