Pták homomorphism theorem revisited

J. R. Ferrer; M. López Pellicer; L. M. Sánchez Ruiz

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 2, page 341-346
  • ISSN: 0011-4642

Abstract

top
Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.

How to cite

top

Ferrer, J. R., López Pellicer, M., and Ruiz, L. M. Sánchez. "Pták homomorphism theorem revisited." Czechoslovak Mathematical Journal 50.2 (2000): 341-346. <http://eudml.org/doc/30565>.

@article{Ferrer2000,
abstract = {Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.},
author = {Ferrer, J. R., López Pellicer, M., Ruiz, L. M. Sánchez},
journal = {Czechoslovak Mathematical Journal},
keywords = {homomorphism theorem B-complete space; B-complete space; homomorphism theorem; B-complete space},
language = {eng},
number = {2},
pages = {341-346},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Pták homomorphism theorem revisited},
url = {http://eudml.org/doc/30565},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Ferrer, J. R.
AU - López Pellicer, M.
AU - Ruiz, L. M. Sánchez
TI - Pták homomorphism theorem revisited
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 2
SP - 341
EP - 346
AB - Rodrigues’ extension (1989) of the classical Pták’s homomorphism theorem to a non-necessarily locally convex setting stated that a nearly semi-open mapping between a semi-B-complete space and an arbitrary topological vector space is semi-open. In this paper we study this extension and, as a consequence of the results obtained, provide an improvement of Pták’s homomorphism theorem.
LA - eng
KW - homomorphism theorem B-complete space; B-complete space; homomorphism theorem; B-complete space
UR - http://eudml.org/doc/30565
ER -

References

top
  1. Topological Vector Spaces. Lecture Notes in Math. 639, Springer Verlag, 1978. (1978) MR0487376
  2. Locally Convex Spaces. Lecture Notes in Math. 331, Springer-Verlag, 1973. (1973) MR0482027
  3. Topological Vector Spaces, Springer-Verlag, 1969. (1969) 
  4. 10.1017/S144678870003175X, J. Austral. Math. Soc. Ser. A 47 (1989), 322–333. (1989) MR1008846DOI10.1017/S144678870003175X
  5. Some new classes of topological vector spaces with closed graph theorems, Comment. Math. Univ. Carolin. 32 (1991), 287–296. (1991) Zbl0778.46006MR1137790
  6. Condiciones de tonelación en espacios vectoriales topológicos, Tesis Doctoral, Universidad de Valencia (1988). (1988) MR2714480
  7. On the Banach-Steinhaus theorem between topological vector spaces and locally convex spaces, Math. Japon. 36 (1991), 143–145. (1991) MR1093364
  8. On the closed graph theorem between topological vector spaces and Fréchet spaces, Math. Japon. 36 (1991), 271–275. (1991) MR1095740
  9. On completeness and the closed graph theorem, Math. Japon. 36 (1991), 891–894. (1991) MR1128440
  10. Topological Vector Spaces Without Local Convexity Conditions, Functional Analysis with Current Applications in Science, Technology and Industry, M. Brokate and A. H. Siddiqi, Editors. Pitman RNMS, Longman, 1998, pp. 37–48. (1998) MR1607876
  11. Topological Vector Spaces, Springer-Verlag, 1986. (1986) MR0342978

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.