COMPLETE METRIC SPACE #complete #metric $space
COMPLETE METRIC SPACE : A metric space X with the metric d is called a complete metric space if every cauchy sequence in x converges in X. ∴ For Example : 1. consider the metric space (0,1) and {1/n} is a cauchy sequence in (0,1). We know that the sequence {1/n} converges to 0. since this limit point 0 does not lies in (0,1) , (0,1) is not a complete metric space. Instead of (0,1) if we consider the metric space [0,1], th...