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Homomorphisms on Topological Groups from the Perspective of Bourbaki-boundedness

Iranian Journal of Mathematical Sciences and Informatics, ISSN: 2008-9473, Vol: 17, Issue: 2, Page: 45-58
2022
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Article Description

In this note we study some topological properties of bounded sets and Bourbaki-bounded sets. Also we introduce two types of Bourbaki-bounded homomorphisms on topological groups including, n−Bourbaki-bounded homomorphisms and B−Bourbaki-bounded homomorphisms. We compare them to each other and with the class of continuous ho-momorphisms. So, two topologies are presented on them and we de-termine some properties on domain and range spaces led to Bourbaki-completeness some of these classes of homomorphisms with the given topologies. At the end of this note we focus on n-compact homomor-phisms and B-compact homomorphisms briefly.

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