Geodesic
On the Internal Duality Between Topological Modules and Bornological Modules
Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 113-119.

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In this paper the internal duality between topological modules and bornological modules is discussed, such a duality being expressed by an equivalence of suitable categories. 
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Bernardes, Nilson C. jun.; Pombo, Dinamérico P. jun. On the Internal Duality Between Topological Modules and Bornological Modules. Bollettino della Unione matematica italiana, Série 9, Tome 5 (2012) no. 1, pp. 113-119. http://geodesic.mathdoc.fr/item/BUMI_2012_9_5_1_a5/

[1] M. Akkar, Espaces vectoriels bornologiques K-convexes, Indag. Math. 73 (1970), 82-95. | MR | Zbl

[2] L. R. Barboza De Oliveira, Les bornologies linéaires et le concept d'absorption linéaire, C. R. Acad. Sci. Paris 278 (1974), 1551-1552. | MR | Zbl

[3] L. R. Barboza De Oliveira, Compatibilité entre bornologies linéaires et topologies linéaires, C. R. Acad. Sci. Paris 278 (1974), 1585-1586. | MR | Zbl

[4] N. C. Bernardes Jr. - D. P. Pombo Jr., Bornological topological modules, Math. Japonica 40 (1994), 455-459. | MR | Zbl

[5] N. C. Bernardes Jr. - D. P. Pombo JR., Mackey convergence and bornological topological modules, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 21 (2010), 299-304. | DOI | MR | Zbl

[6] N. Bourbaki, Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier 2 (1950), 5-16. | fulltext EuDML | MR | Zbl

[7] H. Buchwalter, Topologies, bornologies et compactologies, Publ. Dép. Math. Lyon (1968). | fulltext EuDML | MR

[8] H. Hogbe-Nlend, Théorie des Bornologies et Applications, Lecture Notes in Mathematics 213, Springer-Verlag (1971). | MR | Zbl

[9] H. Hogbe-Nlend, Distributions et Bornologie, Notas Inst. Mat. Estat. Univ. São Paulo, Sér. Mat. 3 (1973). | MR

[10] H. Hogbe-Nlend, Bornologies and Functional Analysis, Notas de Matemática 62, North-Holland (1977). | MR | Zbl

[11] A. Kolmogoroff, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Studia Math. 5 (1934), 29-33. | fulltext EuDML | Zbl

[12] G. W. Mackey, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155-207. | DOI | MR | Zbl

[13] S. Mac Lane, Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer-Verlag (1971). | MR | Zbl

[14] L. Nachbin, Espaços Vetoriais Topológicos, Notas de Matemática 4, Livraria Boffoni (1948). | MR

[15] J. Von Neumann, On complete topological linear spaces, Trans. Amer. Math. Soc. 37 (1935), 1-20. | DOI | MR | Zbl

[16] D. P. Pombo Jr., Linear topologies and linear bornologies on modules, J. Indian Math. Soc. 59 (1993), 107-117; errata ibid. 60 (1994), 191. | MR | Zbl

[17] D. P. Pombo Jr., Module bornologies, Comment. Math. (Prace Mat.) 36 (1996), 179- 188. | MR | Zbl

[18] J. B. Prolla, Topics in Functional Analysis over Valued Division Rings, Notas de Matemática 89, North-Holland (1982). | MR | Zbl

[19] Séminaire Banach, Lecture Notes in Mathematics 277, Springer-Verlag (1972). | MR

[20] C. Voigt, Bornological quantum groups, Pacific J. Math. 235 (2008), 93-135. | DOI | MR | Zbl

[21] L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Mathematics 230, Springer-Verlag (1971). | MR | Zbl

[22] S. Warner, Topological Fields, Notas de Matemática 126, North-Holland (1989). | MR