Lupianez, Francisco (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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Official URL: http://www.sciencedirect.com/science/article/pii/S0377042700006178
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 11:49 |
| Last Modified: | 22 May 2012 11:49 |
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