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The resulting topological space, sometimes written Rl and called the Sorgenfrey line after Robert Sorgenfrey, often serves as a useful counterexample in general topology, like the Cantor set and the long line.
In descriptive set theory and general topology, Luzin space or Luzin set, a hypothetical uncountable topological T1 space without isolated points in which every nowhere-dense subset is at most countable
Bourbaki, Nicolas; Elements of Mathematics: General Topology, Addison-Wesley (1966).