Gallego Lupiáñez, Francisco2023-06-202023-06-202001M.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) 1–14.0377-042710.1016/S0377-0427(00)00617-8https://hdl.handle.net/20.500.14352/57253We 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.engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0377042700006178http://www.sciencedirect.comrestricted access511515.1Continued fractionsTopologyOpen basisTeoría de númerosTopología1205 Teoría de Números1210 Topología