Diophantine Approximation in Metric Space
MFO Scientific ProgramResearch in Pairs 2020
Fraser, Jonathan M.
Ramírez, Felipe A.
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Diophantine approximation is traditionally the study of how well real numbers are approximated by rationals. We propose a model for studying Diophantine approximation in an arbitrary totally bounded metric space where the rationals are replaced with a countable hierarchy of “well-spread” points, which we refer to as $abstract$ $rationals$. We prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness