Continuity

H. S. M. Coxeter and George Beck
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H. S. M. Coxeter: University of Toronto, Department of Mathematics

Chapter Chapter 10 in The Real Projective Plane, 1993, pp 147-154 from Springer

Abstract: Abstract The purpose of this chapter is to show how, in the presence of the axioms of incidence and order, one very simple statement about limits will suffice for the derivation of all the celebrated properties of the one-dimensional continuum, including the axioms of Archimedes and Dedekind, and Enriques’s theorem (our 3·51). This treatment may be regarded as the geometrical counterpart of Weierstrass’s theory of irrational numbers.

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2734-2_10

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DOI: 10.1007/978-1-4612-2734-2_10

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