In mathematical set theory, the Cantor tree is either the full binary tree of height ω + 1, or a topological space related to this by joining its points with intervals.
It was introduced by Robert Lee Moore in the late 1920s as an example of a non-metrizable Moore space (Jones 1966 ).
Jones, F. Burton (1966), "Remarks on the normal Moore space metrization problem", in Bing, R. H.; Bean, R. J. (eds.), Topology Seminar, Wisconsin, 1965 Princeton University Press , pp. 115– 152, ISBN 978-0-691-08056-7 MR 0202100 Nyikos, Peter (1989), "The Cantor tree and the Fréchet–Urysohn property", in Ralph Kopperman; Prabudh Misra; Jack Reichman; Arron R. Todd (eds.), Papers on general topology and related category theory and topological algebra (New York, 1985/1987) 109–123 , doi :10.1111/j.1749-6632.1989.tb22391.x , ISBN 978-0-89766-516-2 MR 1020779 Steen, Lynn Arthur ; Seebach, J. Arthur Jr. (1995) [1978], Counterexamples in Topology Dover reprint of 1978 ed.), Berlin, New York: Springer-Verlag , ISBN 978-0-486-68735-3 MR 0507446