a complete subspace of a metric space is closed
Let be a point in the closure of . Then by the definition of closure, from each ball centered in , we can select a point . This is clearly a Cauchy sequence in , and its limit is , hence by the completeness of , and thus .
|Title||a complete subspace of a metric space is closed|
|Date of creation||2013-03-22 16:31:29|
|Last modified on||2013-03-22 16:31:29|
|Last modified by||ehremo (15714)|