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