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The continuum as a formal space |
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| Authors: | Sara Negri Daniele Soravia |
| Affiliation: | (1) Department of Philosophy, P.O. Box 24 (Unioninkatu 40), 00014 University of Helsinki, Helsinki, Finland. e-mail: negri@helsinki.fi , FI;(2) Dipartimento di Matematica Pura ed Applicata, Via Belzoni 7, I-35131 Padova, Italy. e-mail: srvdnl18@stud10.math.unipd.it , IT |
| 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. Received: 11 November 1996 |
| Keywords: | Mathematics Subject Classification (1991):03F65 26E40 54A05 (Other constructive mathematics Constructive real analysis Topological spaces and generalizations). |
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