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Bernardes, Nilson C. jun. and Pombo, Dinamérico P. jun.:
On the Internal Duality Between Topological Modules and Bornological Modules
Bollettino dell'Unione Matematica Italiana Serie 9 5 (2012), fasc. n.1, p. 113-119, (English)
pdf (245 Kb), djvu (73 Kb). | MR 2919651 | Zbl 1259.46042

Sunto

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.
Referenze Bibliografiche
[1] M. AKKAR, Espaces vectoriels bornologiques K-convexes, Indag. Math. 73 (1970), 82-95. | MR 262795 | Zbl 0191.12802
[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 355508 | Zbl 0284.46048
[3] L. R. BARBOZA DE OLIVEIRA, Compatibilité entre bornologies linéaires et topologies linéaires, C. R. Acad. Sci. Paris 278 (1974), 1585-1586. | MR 355509 | Zbl 0284.46049
[4] N. C. BERNARDES JR. - D. P. POMBO JR., Bornological topological modules, Math. Japonica 40 (1994), 455-459. | MR 1305539 | Zbl 0822.46060
[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. | fulltext (doi) | MR 2677607 | Zbl 1198.46041
[6] N. BOURBAKI, Sur certains espaces vectoriels topologiques, Ann. Inst. Fourier 2 (1950), 5-16. | fulltext EuDML | MR 42609 | Zbl 0042.35302
[7] H. BUCHWALTER, Topologies, bornologies et compactologies, Publ. Dép. Math. Lyon (1968). | fulltext EuDML | MR 412762
[8] H. HOGBE-NLEND, Théorie des Bornologies et Applications, Lecture Notes in Mathematics 213, Springer-Verlag (1971). | MR 625157 | Zbl 0225.46005
[9] H. HOGBE-NLEND, Distributions et Bornologie, Notas Inst. Mat. Estat. Univ. São Paulo, Sér. Mat. 3 (1973). | MR 463909
[10] H. HOGBE-NLEND, Bornologies and Functional Analysis, Notas de Matemática 62, North-Holland (1977). | MR 500064 | Zbl 0359.46004
[11] A. KOLMOGOROFF, Zur Normierbarkeit eines allgemeinen topologischen linearen Raumes, Studia Math. 5 (1934), 29-33. | fulltext EuDML | Zbl 60.1229.02
[12] G. W. MACKEY, On infinite-dimensional linear spaces, Trans. Amer. Math. Soc. 57 (1945), 155-207. | fulltext (doi) | MR 12204 | Zbl 0061.24301
[13] S. MAC LANE, Categories for the Working Mathematician, Graduate Texts in Mathematics 5, Springer-Verlag (1971). | MR 1712872 | Zbl 0232.18001
[14] L. NACHBIN, Espaços Vetoriais Topológicos, Notas de Matemática 4, Livraria Boffoni (1948). | MR 29470
[15] J. VON NEUMANN, On complete topological linear spaces, Trans. Amer. Math. Soc. 37 (1935), 1-20. | fulltext (doi) | MR 1501776 | Zbl 0011.16403
[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 1248951 | Zbl 0860.16031
[17] D. P. POMBO JR., Module bornologies, Comment. Math. (Prace Mat.) 36 (1996), 179- 188. | MR 1427832 | Zbl 0901.46003
[18] J. B. PROLLA, Topics in Functional Analysis over Valued Division Rings, Notas de Matemática 89, North-Holland (1982). | MR 688308 | Zbl 0506.46059
[19] Séminaire Banach, Lecture Notes in Mathematics 277, Springer-Verlag (1972). | MR 372566
[20] C. VOIGT, Bornological quantum groups, Pacific J. Math. 235 (2008), 93-135. | fulltext (doi) | MR 2379773 | Zbl 1157.46041
[21] L. WAELBROECK, Topological Vector Spaces and Algebras, Lecture Notes in Mathematics 230, Springer-Verlag (1971). | MR 467234 | Zbl 0225.46001
[22] S. WARNER, Topological Fields, Notas de Matemática 126, North-Holland (1989). | MR 1002951

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