Cao, JGreenwood, S2011-11-112011-11-1120062006Applied General Topology, vol.7(2), pp.253 - 2641576-9402 (print)https://hdl.handle.net/10292/2512In this paper, we consider the ideal I¾ generated by all ¾-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that I¾ is compatible with the topology for any given topological space, an analogue to the Banach category theorem. Some applications of this result and the Banach category theorem are also given.Copyright © 2006 Applied General Topology - http://agt.webs.upv.es. All rights reserved. By special permission authors retain the right to place his/her publication version of the work on a personal website or institutional repository for non commercial purposes. The definitive version was published in (see Citation). The original publication is available at (see Publisher’s Version).CompatibleIdealResolvable¾-nowhere denseVolterraWeakly VolterraJournal ArticleOpenAccess9724