Share
Explore BrainMass

Metric Spaces of a nonempty set

(See attached file for full problem description)

1. Show that the functions d defined below satisfy the properties of a metric.

a. Let X be any nonempty set and let d be defined by The d is the call the discrete metric.
b. If X is the set of all m-tuples of real numbers and, if for and , then (X,d) is a metric space.
c. Let X be the set of all real-valued frunctions which are defined and continuous on the closed interval [a,b] in and let

Attachments

Solution Summary

This solution is comprised of a detailed explanation to show that the functions d defined below satisfy the properties of a metric.

$2.19