- #1
shoescreen
- 15
- 0
Hi,
I have been reading about metric spaces and came across an elementary property that I am having difficulty proving. A quick search on these forums and google has also failed.
Given a metric space with distance function [itex]d[/itex], and an increasing, concave function [itex]f:\mathbb{R} \rightarrow \mathbb{R}[/itex] so that [itex]f(0)=0[/itex], show that [itex]f\circ d[/itex] is a metric.
Of course, only the triangle inequality is nontrivial.
I have been reading about metric spaces and came across an elementary property that I am having difficulty proving. A quick search on these forums and google has also failed.
Given a metric space with distance function [itex]d[/itex], and an increasing, concave function [itex]f:\mathbb{R} \rightarrow \mathbb{R}[/itex] so that [itex]f(0)=0[/itex], show that [itex]f\circ d[/itex] is a metric.
Of course, only the triangle inequality is nontrivial.