Talk:Closed Subset of Real Numbers with Lower Bound contains Infimum

Do we also need to invoke a result that shows that closure in the Metric Space sense is the same as closure in the Topological sense? Or should we use a proof which demonstrates that a closed set equals its closure as defined in the context of a metric space without invoking the concept of "topological closure"? --prime mover (talk) 15:21, 29 July 2015 (UTC)