Two metrics d, p on a set X are said to be equivalent if they define...

Transcribed Image Text:

Two metrics d, p on a set X are said to be equivalent if they define the same convergent sequences. Show that for any metric space (x, d), d(a, b) 1+d(a, b) p(a, b) : defines an equivalent metric. Two metrics d, p on a set X are said to be equivalent if they define the same convergent sequences. Show that for any metric space (x, d), d(a, b) 1+d(a, b) p(a, b) : defines an equivalent metric.