Time metric spaces a framework for time sensitive distance

Abstract

Distance is no longer measured only in traditional units such as kilometers or miles, but is better understood as a time-sensitive concept. We introduce time-metric spaces where distance reflects a dynamic time-dependent cost influenced by absolute time, history of paths taken, or environmental factors. When this cost (distance) is independent of time, the structure becomes a classical metric space. Time-metric spaces extend metric theory to describe systems where distance is measured in minutes and not in meters, and provide a natural way to model evolving time-dependent phenomena.