A regularity property of sets that subsumes all other classical regularity properties is that of being determined. For simplicity, we shall work with the Baire space \(\mathcal{N}\). Recall that the elements of \(\mathcal{N}\) are functions \(f:\mathbb{N} \to \mathbb{N}\), that is, sequences of natural numbers of length \(\omega\). The space \(\mathcal{N}\) is topologically equivalent (i.e., homeomorphic) to the set of irrational points of \(\mathbb{R}\). So, since we are interested in the regularity properties of subsets of \(\mathbb{R}\), and since countable sets, such as the set of rationals, are negligible in terms of those properties, we may as well work with \(\mathcal{N}\), instead of \(\mathbb{R}\).