|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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