The ideal generated by sigma-nowhere dense sets
Cao, J; Greenwood, S
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In 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.