SHALLOWLY DISCUSSION ON THE RELATION OF METRIC FUNCTION AND REDUCED METRIC FUNCTION IN METRIC SPACE

This paper mainly studies the relation of metric function and reduced metric functionin in metric space.This paper defines the concept and characteristic of partition,densification partition,rectifiable curve and curve length.Ulteriorly,the paper proves these characteristic.Imitating Riemannian geometry,the paper defines reduced metric in metric space via metric function in metric space.Finally,the paper prove reduced distance is not less than distance between two points in metric space.