Diophantine approximation in metric space

This is the authors' abstract. We don't add key points for this paper.

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.