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.
@article{BUMI_2012_9_5_1_113_0, author = {Nilson C. jun. Bernardes and Dinam\'erico P. jun. Pombo}, title = {On the Internal Duality Between Topological Modules and Bornological Modules}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {5}, year = {2012}, pages = {113-119}, zbl = {1259.46042}, mrnumber = {2919651}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2012_9_5_1_113_0} }
Bernardes, Nilson C. jun.; Pombo, Dinamérico P. jun. On the Internal Duality Between Topological Modules and Bornological Modules. Bollettino dell'Unione Matematica Italiana, Tome 5 (2012) pp. 113-119. http://gdmltest.u-ga.fr/item/BUMI_2012_9_5_1_113_0/
[1] Espaces vectoriels bornologiques K-convexes, Indag. Math.73 (1970), 82-95. | MR 262795 | Zbl 0191.12802
,[2] Les bornologies linéaires et le concept d'absorption linéaire, C. R. Acad. Sci. Paris278 (1974), 1551-1552. | MR 355508 | Zbl 0284.46048
,[3] Compatibilité entre bornologies linéaires et topologies linéaires, C. R. Acad. Sci. Paris278 (1974), 1585-1586. | MR 355509 | Zbl 0284.46049
,[4] Bornological topological modules, Math. Japonica 40 (1994), 455-459. | MR 1305539 | Zbl 0822.46060
- ,[5] Mackey convergence and bornological topological modules, Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 21 (2010), 299-304. | MR 2677607 | Zbl 1198.46041
- JR.,[6] Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier2 (1950), 5-16. | MR 42609 | Zbl 0042.35302
,[7] Topologies, bornologies et compactologies, Publ. Dép. Math. Lyon (1968). | MR 412762
,[8] 213, Springer-Verlag (1971). | MR 625157 | Zbl 0225.46005
, Théorie des Bornologies et Applications, Lecture Notes in Mathematics[9] Distributions et Bornologie, Notas Inst. Mat. Estat. Univ. São Paulo, Sér. Mat. 3 (1973). | MR 463909
,[10] 62, North-Holland (1977). | MR 500064 | Zbl 0359.46004
, Bornologies and Functional Analysis, Notas de Matemática[11] Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Studia Math.5 (1934), 29-33. | Zbl 60.1229.02
,[12] On infinite-dimensional linear spaces, Trans. Amer. Math. Soc.57 (1945), 155-207. | MR 12204 | Zbl 0061.24301
,[13] 5, Springer-Verlag (1971). | MR 1712872 | Zbl 0232.18001
, Categories for the Working Mathematician, Graduate Texts in Mathematics[14] 4, Livraria Boffoni (1948). | MR 29470
, Espaços Vetoriais Topológicos, Notas de Matemática[15] On complete topological linear spaces, Trans. Amer. Math. Soc.37 (1935), 1-20. | MR 1501776 | Zbl 0011.16403
,[16] Linear topologies and linear bornologies on modules, J. Indian Math. Soc.59 (1993), 107-117; errata ibid. 60 (1994), 191. | MR 1248951 | Zbl 0860.16031
,[17] Module bornologies, Comment. Math. (Prace Mat.) 36 (1996), 179- 188. | MR 1427832 | Zbl 0901.46003
,[18] 89, North-Holland (1982). | MR 688308 | Zbl 0506.46059
, Topics in Functional Analysis over Valued Division Rings, Notas de Matemática[19] Séminaire Banach, Lecture Notes in Mathematics277, Springer-Verlag (1972). | MR 372566
[20] Bornological quantum groups, Pacific J. Math.235 (2008), 93-135. | MR 2379773 | Zbl 1157.46041
,[21] 230, Springer-Verlag (1971). | MR 467234 | Zbl 0225.46001
, Topological Vector Spaces and Algebras, Lecture Notes in Mathematics[22] 126, North-Holland (1989). | MR 1002951
, Topological Fields, Notas de Matemática