International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 1, Pages 189-191
Two large subsets of a functional space
Department of Mathematics, Portland State University, Portland 97207, Oregon, USA
Received 29 May 1984
Copyright © 1985 F. S. Cater. 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.
Let denote the Banach space composed of all bounded derivatives of everywhere differentiable functions on such that the set of points where vanishes is dense in . Let consist of those functions in that are unsigned on every interval, and let consist of those functions in that vanish on dense subsets of measure zero. Then and are dense -subsets of with void interior. Neither nor is a subset of the other.