By definition of a Baire space, such sets ( called " residual sets " ) are dense.
2.
When the algorithm converges on a stable residual set, a final decision list of the target word is obtained.
3.
For applications, if a property holds on a residual set, it may not hold for every point, but perturbing it slightly will generally land one inside the residual set ( by nowhere density of the components of the meagre set ), and these are thus the most important case to address in theorems and algorithms.
4.
For applications, if a property holds on a residual set, it may not hold for every point, but perturbing it slightly will generally land one inside the residual set ( by nowhere density of the components of the meagre set ), and these are thus the most important case to address in theorems and algorithms.
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