Applied Mathematics & Information Sciences

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In this work, we study new structure in algebraic bornological structures, its called semi bornological groups, so the problem of boundedness for this kind of groups, which cannot bornologize because the product map is not bounded was solved. Additionally, we stydy further properties of semi bornological groups. In particular, we show that every left (right) translations in semi bornological groups are bornological isomorphisms. Therefor, the semi bornological groups are homogeneous. Furthermore, to find the sufficient condition on the left bornological group or right bornological group to be semi bornological group was investigated. However, we gave the sufficient condition to make any semi bornological group to be bornological groups. Finally, in contrast with semi bornological group, we show that bornological semi group is not homogenous space

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