Skip Navigation

Journal of the London Mathematical Society 1996 53(1):158-166; doi:10.1112/jlms/53.1.158
© 1996 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Saxon, S. A.
Right arrow Articles by Ruiz, L. M. S.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Barrelled Countable Enlargements and the Bounding Cardinal

S. A. Saxon and L. M. Sánchez Ruiz

Department of Mathematics, University of Florida PO Box 8000, Gainesville, Florida 32611-8000, USA
EUITI-Departamento de Matemática Aplicada, Universidad Politécnica de Valencia 46071 Valencia, Spain

Received 4 October 1993.

Replacing c with the bounding cardinal b improves two standard BCE results of Robertson, Tweddle and Yeomans, and b is optimal for the BCE codimension/inheritance result of Bonet and Pérez Carreras. Indeed, b is the smallest infinite-dimensionality for metrizable barrelled spaces, and is the largest cardinal {kappa} such that every subspace of codimension less than {kappa} in a metrizable barrelled space is itself barrelled. We thus reconfirm b as one of two ‘optimal cardinals for metrizable barrelled spaces’. Esthetically pleasing, these properties of b immediately solve the normable BCE problem without extra-ZFC axiomatic assumptions, reduce the separable quotient problem to Banach spaces E with b ≤ density character of E ≤ c, and are part of the solution to one version of the metrizable BCE problem found in our sequel, devoted to the other ‘optimal cardinal’.

This paper was started while the second author stayed at the University of Florida supported by DGICYT BE91-332, later being partially supported by DGICYT PB91-0407.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.