Metric spaces in synthetic topology

@article{Bauer2012MetricSI,
  title={Metric spaces in synthetic topology},
  author={Andrej Bauer and Davorin Lesnik},
  journal={Ann. Pure Appl. Logic},
  year={2012},
  volume={163},
  pages={87-100}
}
Abstract We investigate the relationship between the synthetic approach to topology, in which every set is equipped with an intrinsic topology, and constructive theory of metric spaces. We relate the synthetic notion of compactness of Cantor space to Brouwer’s Fan Principle. We show that the intrinsic and metric topologies of complete separable metric spaces coincide if they do so for Baire space. In Russian Constructivism the match between synthetic and metric topology breaks down, as even a… CONTINUE READING

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