Abstract and Applied Analysis
Volume 2005 (2005), Issue 3, Pages 221-227
Inscribing closed non--lower porous sets into Suslin
non--lower porous sets
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8 186 75, Czech Republic
Received 28 April 2004
Copyright © 2005 Luděk Zajíček and Miroslav Zelený. 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 main aim of this paper is to prove that every
non--lower porous Suslin set in a topologically complete
metric space contains a closed non--lower porous subset.
In fact, we prove a general result of this type on “abstract
porosities.” This general theorem is also applied to ball small
sets in Hilbert spaces and to -cone-supported sets in separable Banach spaces.