Abstract.
A constructive definition of the continuum based on formal topology is given and its basic properties studied. A natural notion of Cauchy sequence is introduced and Cauchy completeness is proved. Other results include elementary proofs of the Baire and Cantor theorems. From a classical standpoint, formal reals are seen to be equivalent to the usual reals. Lastly, the relation of real numbers as a formal space to other approaches to constructive real numbers is determined.
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Received: 11 November 1996
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Negri, S., Soravia, D. The continuum as a formal space. Arch Math Logic 38, 423–447 (1999). https://doi.org/10.1007/s001530050149
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DOI: https://doi.org/10.1007/s001530050149