The reals as rational Cauchy filters

Weiss, Ittay (2016) The reals as rational Cauchy filters. New Zealand Journal of Mathematics, 46 . pp. 21-51. ISSN 1171-6096

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Abstract

We present a detailed and elementary construction of the real
numbers from the rational numbers a la Bourbaki. The real numbers are defined to be the set of all minimal Cauchy filters in Q (where the Cauchy condition is defined in terms of the absolute value function on Q) and are proven directly, without employing any of the techniques of uniform spaces, to form a complete ordered field. The construction can be seen as a variant of Bachmann’s construction by means of nested rational intervals, allowing for a canonical choice of representatives

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Technology and Environment (FSTE)
Depositing User:	Ittay Weiss
Date Deposited:	25 Jul 2016 02:16
Last Modified:	25 Jul 2016 02:16
URI:	https://repository.usp.ac.fj/id/eprint/8818

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