Preprint Article Version 1 This version is not peer-reviewed

Further Properties of Bornological Groups

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 (doi: 10.20944/preprints201704.0039.v1). Imran, A.N.; Rakhimov, I.S. Further Properties of Bornological Groups. Preprints 2017, 2017040039 (doi: 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.

Subject Areas

bornological set; bornological group

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