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Continued fractions and order-preserving homeomorphism.

Lupianez, Francisco Gallego (2001) Continued fractions and order-preserving homeomorphism. Journal of Computational and Applied Mathematics, 136 (1-2). pp. 255-258. ISSN 0377-0427

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Abstract

We study in this paper a modification of continued fractions defined by the author, such that its lexicographic order coincides with the linear order of real numbers. This fact has beautiful consequences in Topology. Indeed, it gives the possibility to construct a nice open basis for the Sorgenfrey line.

Item Type:Article
Uncontrolled Keywords:Continued fractions; Topology; Open basis
Subjects:Sciences > Mathematics > Number theory
Sciences > Mathematics > Topology
ID Code:15302
References:

M.Khalouani, S.Labhalla, H.Lombardi, L Etude constructive de problMemes de topologie pour les rLeels irrationnels, Math.Logic Quart.45 (1999) 257–288.

S.Labhalla, H.Lombardi, Real numbers, continued fractions and complexity classes, Ann.Pure Appl.Logic 50 (1990) 1–28.

F.G. LupiLa˜nez, On continued fractions and the Sorgenfrey line, Quest.& Ans.Gen.Topology 8 (1990) 457–465.

N.Lusin, Sur les emsembles analytiques, Fund.Math.10 (1927) 1–95.

H.J.S. Smith, Note on continued fractions, Messenger Math. 6 (1877) 1–14.

Deposited On:22 May 2012 09:49
Last Modified:06 Feb 2014 10:21

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