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Further Properties of Bornological Groups
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Version 1
: Received: 6 April 2017 / Approved: 7 April 2017 / Online: 7 April 2017 (04:17:16 CEST)
How to cite: Imran, A.N.; Rakhimov, I.S. Further Properties of Bornological Groups. Preprints 2017, 2017040039. https://doi.org/10.20944/preprints201704.0039.v1 Imran, A.N.; Rakhimov, I.S. Further Properties of Bornological Groups. Preprints 2017, 2017040039. https://doi.org/10.20944/preprints201704.0039.v1
Abstract
In this work, Further properties of bornological groups are studied to find the sufficient conditions to introduce a bornology on a group. In particular, we show that every left (right) translations in bornological groups are isomorphisms and therefore the bornological group's structures are homogeneous, and this property from the bornological group is not shared with bornological semigroups. Further, the boundedness of a bornological group can be deduced from its boundedness at the identity.
Keywords
bornological set; bornological group
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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