Cantor tree

For the surface, see Cantor tree surface.

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).

References

• Jones, F. Burton (1966), "Remarks on the normal Moore space metrization problem", in Bing, R. H.; Bean, R. J. (eds.), Topology Seminar, Wisconsin, 1965, Annals of Mathematics Studies, vol. 60, 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", Papers on general topology and related category theory and topological algebra (New York, 1985/1987), Ann. New York Acad. Sci., vol. 552, New York: New York Acad. Sci., pp. 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