Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.
Density measures for language generation
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Banach density of generated languages: Dichotomies in topology and dimension
Banach density reveals topological dichotomies in language generation: 1/2 is always achievable in 1D for finite-rank spaces but impossible in some infinite-rank cases, unlike asymptotic density; d>=2 needs nondegeneracy.