The ideal generated by $sigma$-nowhere dense sets

Jiling Cao and Sina Greenwood


In this paper, we consider the ideal $mathscr I_sigma$ generated by all $sigma$-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that $mathscr I_sigma$ is compatible with the topology for any given space, an analogue to the Banach category theorem. Some applications of this result and the Banach category theorem are also given.

Compatible ideal, Ideal, Resolvable, $sigma$-nowhere dense, Volterra, Weakly Volterra.

Math Review Classification
Primary 26A15 ; Secondary 28A05, 54C05, 54E52

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11 pages

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