Diophantine Approximation in Metric Space
MFO Scientific ProgramResearch in Pairs 2020
Fraser, Jonathan M.
Ramírez, Felipe A.
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