Abstract
We consider homomorphisms from a normed space into a topological group. Assuming their boundedness in a neighbourhood (in relative topology) of an extremal point of the unit sphere, we derive their linearity (whenever it makes sense), closedness of the graph or continuity.
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Dedicated to Professor János Aczél on his 85th birthday
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Ger, R., Sablik, M. Homomorphisms and boundedness in topological groups. Aequat. Math. 80, 119–130 (2010). https://doi.org/10.1007/s00010-010-0028-z
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DOI: https://doi.org/10.1007/s00010-010-0028-z