The paper explains bornological sets and groups for boundedness in mathematical contexts, suggesting ideas for ideal conditions.
In this work, we explain the basic concepts of bornological structures bornological sets and bornological groups, that solve the problems of boundedness for sets and groups. with some examples and fundamental construction for this structure such as bornological subset, product bornology, bornological isomorphism, and proof Every matrix’s space is bornological set. Also explain ideal bornological . The motivation for this part is to require less restrictive condition of boundedness correctly ideal.
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Imran et al. (2025) studied this question.
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