Super-dense sets coincide with co-meager Baire-property sets; non-normal numbers are super-dense while normal numbers are not, enabling explicit computable continuous maps from normal to non-normal numbers and an algorithm for non-normality closed under countable continuous images.
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Super-Dense Sets and Their Role in the Theory of Normal Numbers
Super-dense sets coincide with co-meager Baire-property sets; non-normal numbers are super-dense while normal numbers are not, enabling explicit computable continuous maps from normal to non-normal numbers and an algorithm for non-normality closed under countable continuous images.