Application Of Cauchy Sequence In Investigating The Completeness Of A Metric Space:- Solomon Chidera E

ABSTRACT In this research work “Application Of Cauchy Sequence In Investigating The Completeness Of A Metric Space”, we examined the definition of Cauchy sequence and illustrated this with specific examples. We also reviewed some properties of Cauchy sequence that help to exert completeness of a metric space and illustrated those properties with proves. Furthermore, we defined metric spaces and illustrated it with specific examples. Inequalities like the Holder, Cauchy Schwartz and Minkowski relevant in proving the triangle inequality property of metric spaces were explored. Finally, Cauchy sequence were used to determine the completeness or otherwise ofsome metric spaces.