International Journal of Mathematics and Mathematical Sciences
Volume 30 (2002), Issue 8, Pages 449-457
On weighted spaces without a fundamental sequence of bounded sets
Mathematics Department, University of Lagos, Yaba, Lagos, Nigeria
Received 5 February 2001; Revised 21 September 2001
Copyright © 2002 J. O. Olaleru. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The problem of countably quasi-barrelledness of weighted spaces of continuous functions, of which there are no results in the
general setting of weighted spaces, is tackled in this paper.
This leads to the study of quasi-barrelledness of weighted spaces
in which, unlike that of Ernst and Schnettler (1986), though with
a similar approach, we drop the assumption that the weighted
space has a fundamental sequence of bounded sets. The study of
countably quasi-barrelledness of weighted spaces naturally leads
to definite results on the weighted (DF)-spaces for those
weighted spaces with a fundamental sequence of bounded sets.