The Arzelà-Ascoli Theorem

  • Ben Galin
  • Published 2006


In Euclidean space, the Heine-Borel Theorem provides us with an elegant method of determining whether a given set is compact: one need only check if the set is closed and bounded. This allows not only for a practical way of proving compactness, but also builds an intuitive understanding of what compactness means in Euclidean space. However, the Heine-Borel… (More)