The ideal generated by σ-nowhere dense sets

Abstract

In this paper, we consider the ideal Iσ 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 Iσ 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.

Keywords

• Compatible
• Ideal
• Resolvable
• σ-nowhere dense
• Volterra
• Weakly Volterra