Compatible topologies and bornologies on modules

Dinamérico Pereira, Jr. Pombo

Commentationes Mathematicae Universitatis Carolinae (1998)

  • Volume: 39, Issue: 2, page 341-352
  • ISSN: 0010-2628

Abstract

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Compatible topologies and bornologies on modules are introduced and studied.

How to cite

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Pombo, Dinamérico Pereira, Jr.. "Compatible topologies and bornologies on modules." Commentationes Mathematicae Universitatis Carolinae 39.2 (1998): 341-352. <http://eudml.org/doc/248222>.

@article{Pombo1998,
abstract = {Compatible topologies and bornologies on modules are introduced and studied.},
author = {Pombo, Dinamérico Pereira, Jr.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {module topologies; continuous linear mappings; module bornologies; bounded linear mappings; equicontinuous sets; equibounded sets; topological modules of linear mappings; module topologies; module bornologies; equicontinuous sets; equibounded sets; topological modules of linear mappings},
language = {eng},
number = {2},
pages = {341-352},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Compatible topologies and bornologies on modules},
url = {http://eudml.org/doc/248222},
volume = {39},
year = {1998},
}

TY - JOUR
AU - Pombo, Dinamérico Pereira, Jr.
TI - Compatible topologies and bornologies on modules
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1998
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 39
IS - 2
SP - 341
EP - 352
AB - Compatible topologies and bornologies on modules are introduced and studied.
LA - eng
KW - module topologies; continuous linear mappings; module bornologies; bounded linear mappings; equicontinuous sets; equibounded sets; topological modules of linear mappings; module topologies; module bornologies; equicontinuous sets; equibounded sets; topological modules of linear mappings
UR - http://eudml.org/doc/248222
ER -

References

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  1. Barboza de Oliveira L.R., Compatibilité entre bornologies linéaires et topologies linéaires, C.R. Acad. Sci. Paris 278 (1974), 1585-1586. (1974) MR0355509
  2. Barboza de Oliveira L.R., Les espaces vectoriels linéairement bornologisés et topologisés, C.R. Acad. Sci. Paris 278 (1974), 1627-1628. (1974) MR0355510
  3. Bernardes N.C., Jr., Pombo D.P., Jr., Bornological topological modules, Math. Japonica 40 (1994), 455-459. (1994) Zbl0822.46060MR1305539
  4. Bourbaki N., Algèbre, Chapter II, 3rd edition, Actualités Scientifiques et Industrielles 1236, Hermann, 1967. Zbl1139.12001
  5. Bourbaki N., Topologie Générale, Chapter II, 4th edition, Actualités Scientifiques et Industrielles 1142, Hermann, 1965. Zbl1107.54001MR0244924
  6. Bourbaki N., Topologie Générale, Chapter X, 2nd edition, Actualités Scientifiques et Industrielles 1084, Hermann, 1967. Zbl1107.54001
  7. Bourbaki N., Espaces Vectoriels Topologiques, Chapter III, Actualités Scientifiques et Industrielles 1229, Hermann, 1967. Zbl1106.46003
  8. Grothendieck A., Dieudonné J., Eléments de Géometrie Algébrique I, Grundlehren der mathematischen Wissenschaften 166, Springer-Verlag, 1971. 
  9. Hogbe-Nlend H., Bornologies and Functional Analysis, Notas de Matemática 62, North-Holland Publishing Company, 1977. Zbl0359.46004MR0500064
  10. Köthe G., Topological Vector Spaces II, Grundlehren der mathematischen Wissenschaften 237, Springer-Verlag, 1979. MR0551623
  11. Pombo D.P., Jr., On the completion of certain topological modules, Math. Japonica 37 (1992), 333-336. (1992) Zbl0761.46041MR1159032
  12. Pombo D.P., Jr., On barrelled topological modules, Internat. J. Math. & Math. Sci. 19 (1996), 45-52. (1996) Zbl0839.46044MR1361975
  13. Pombo D.P., Jr., Module bornologies, Comment. Math. 36 (1996), 179-188. (1996) Zbl0901.46003MR1427832
  14. Schaefer H.H., Topological Vector Spaces, Graduate Texts in Mathematics 3, Springer-Verlag, 1971. Zbl0983.46002MR0342978
  15. HASH(0xa5a1b60), Séminaire Banach, Lecture Notes in Mathematics 277, Springer-Verlag, 1972, . 
  16. Waelbroeck L., Topological Vector Spaces and Algebras, Lecture Notes in Mathematics 230, Springer-Verlag, 1971. Zbl0225.46001MR0467234
  17. Warner S., Topological Fields, Notas de Matemática 126, North-Holland Publishing Company, 1989. Zbl0683.12014MR1002951

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