Literature Nots on Bornological Set and Bornological Group
DOI:
https://doi.org/10.24237/Keywords:
Bounded set, Bounded map, Semi bounded set, Semi bounded map, Bornological Set, Bornological Group.Abstract
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.
References
[1] H. Hogbe-Nlend, Bornologies and Functional Analysis, Math. Studies 26, (North- Holland Publishing Company Netherlands, 1977)
[2] J. S. Farah, Some of Bornological Structures, Thesis University of Diyala, (2021)
[3] F. A. Ashwaq, Soft Bornological Structures, Thesis University of Diyala, (2022)
[4] A. N. Alaa, New Classes of Algebraic Bornological Structures, Thesis University of Diyala, (2022)
[5] O. E. Amal, Fuzzy Bornological Structuresv, Thesis University of Diyala, (2022)
[6] A. D. Naba, Bornological Ideal and New Classes of Bornological Semigroups, Thesis University of Diyala, (2023)
[7] A.N. Imran, Bornological structures on some algebraic system, PHD thesis, UPM university, (2018)
[8] S. Funakosi, Induced Bornological Representations of Bornological Algebras, Portugaliae Mathematica, 35(2), 97- 109(1976)
[9] F. Bambozzi, On a Generalization of Affinioid Varieties, PHD thesis, (2013)
[10] A. N. Imran, Bornological Groupv, Diyala Journal for Pure Sciences, 12, (2013)
[11] A. N. Imran, and I. S. Rakhimov, On Bornological Semigroups, IEEE, proceeding, (2015)
[12] A. N. Imran, I. S. Rakhimov, Further Properties of Bornological Groups, Far East Journal of Mathematical Sciences, 2017040039, Preprints, (2017), DOI(http://dx.doi.org/10.20944/preprints201704.0039.v1)
[13] A. N. Imran, I. S. Rakhimov, and S. K. S. Hussain, Semi-bounded sets with respect to bornological sets, In: AIP Conf. Proc., 1830, (2017), DOI(https://doi.org/10.1063/1.4980974)
[14] A. N. Imran, SKS. Husain, Semi Bornological Groups, In: Journal of Physics: Conference Series, 1366, IOP Publishing, 12071(2019), DOI(10.1088/1742-6596/1366/1/012071)
[15] L. A. Majed, Compare The Category of G-bornological group and G-Topological Group, J. Phys.: Conf. Ser., 1664. 012040, (2020), DOI(10.1088/1742-6596/1664/1/012040
[16] F. Khalil Alhan, Algebraic Bornological Structures, University Diyala, (2021)
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