Tag Archives: Arzela-Ascoli Theorem

Arzela-Ascoli Theorem

1. Motivation of our main Theorem In metric space, topological compactness and sequential compactness are equivalent. In , we have a Heine-Borel property. However, the following example gives that closedness and boundedness do not gurantee the compactness in general. Example 1 This example is related to sequential compactness. Consider and where has 1 at th… Read More »