Cao, JGreenwood, S2011-11-112012-04-022011-11-112012-04-0220062006Applied General Topology, vol.7(2), pp.253 - 2641576-9402https://hdl.handle.net/10292/3562In this paper, we consider the ideal I_σ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that I_σ 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).Compatible idealIdealResolvablesigma-nowhere denseVolterraWeakly VolterraJournal ArticleOpenAccess9724