# Real analysis - open and closed sets

(See attached file for full problem description)

1. In the metric space show that:

a. Any open interval of the form (a,b), (a, ), or (- ,b) is an open set.

b. A close interval [a,b] is a closed set.

c. Any interval of the form [a, ) is a closed set.

https://brainmass.com/math/real-analysis/real-analysis-open-closed-sets-87019

#### Solution Preview

Please see the attachment.

Proof:

(a) For any , we select , then . This implies that is an open set. For any , we ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer in the metric space show that:

$2.19