In mathematical set theory, the Cantor tree is either the full

binary tree In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary t ...

of height ω + 1, or a

topological space In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called points ...

related to this by joining its points with intervals, that was introduced by

Robert Lee Moore Robert Lee Moore (November 14, 1882 – October 4, 1974) was an American mathematician who taught for many years at the University of Texas. He is known for his work in general topology, for the Moore method of teaching university mathematics, ...

in the late 1920s as an example of a non-metrizable Moore space .

References

* * *{{Citation , last1=Steen , first1=Lynn Arthur , author1-link=Lynn Arthur Steen , last2=Seebach , first2=J. Arthur Jr. , author2-link=J. Arthur Seebach, Jr. , title=

Counterexamples in Topology ''Counterexamples in Topology'' (1970, 2nd ed. 1978) is a book on mathematics by topologists Lynn Steen and J. Arthur Seebach, Jr. In the process of working on problems like the metrization problem, topologists (including Steen and Seebach) hav ...

, origyear=1978 , publisher=

Springer-Verlag Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, location=Berlin, New York , edition=

Dover Dover () is a town and major ferry port in Kent, South East England. It faces France across the Strait of Dover, the narrowest part of the English Channel at from Cap Gris Nez in France. It lies south-east of Canterbury and east of Maidstone ...

reprint of 1978 , isbn=978-0-486-68735-3 , mr=507446 , year=1995 Trees (set theory) Topological spaces