Diophantine approximation in metric space

Abstract 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 asabstract rationals. We prove various Jarník–Besicovitch type dimension bounds and investigate their sharpness.