Compactness and Continuity, Constructively Revisited

  title={Compactness and Continuity, Constructively Revisited},
  author={Douglas S. Bridges and Hajime Ishihara and Peter Schuster},
In this paper, the relationships between various classical compactness properties, including the constructively acceptable one of total boundedness and completeness, are examined using intuitionistic logic. For instance, although every metric space clearly is totally bounded whenever it possesses the Heine-Borel property that every open cover admits of a finite subcover, we show that one cannot expect a constructive proof that any such space is also complete. Even the Bolzano-Weierstras… CONTINUE READING