Abstract
In this paper, the concept of a*-sets is introduced and the ideal Ω generated by all <5*-sets in a topological space is considered. Some properties of 5*-sets, the ideal Ω and their relations with resolvability, irresolvability, the Volterra property and other ideals are explored. It is shown that Ω is compatible with the topology for any given space, which is an analogue to the Banach Category theorem.
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