International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 3, Pages 149-165
Boundedness and surjectivity in normed spaces
Department of Mathematics, Agder University College, Servicebox 422, Kristiansand 4604, Norway
Received 24 January 2001; Revised 6 June 2001
Copyright © 2002 Olav Nygaard. 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.
We define the -) boundedness property and the -) surjectivity property for sets in normed spaces. We
show that these properties are pairwise equivalent in complete
normed spaces by characterizing them in terms of a category-like
property called -) thickness. We give examples of
interesting sets having or not having these properties. In
particular, we prove that the tensor product of two
-thick sets in and is a -thick subset in and obtain as a consequence that the set - is -thick.