In mathematics, Erdős space is a topological space named after Paul Erdős, who described it in 1940.
[1] Erdős space is defined as a subspace
of the Hilbert space of square summable sequences, consisting of the sequences whose elements are all rational numbers.
Erdős space is a totally disconnected, one-dimensional topological space.
in the product topology.
If the set of all homeomorphisms of the Euclidean space
) that leave invariant the set
of rational vectors is endowed with the compact-open topology, it becomes homeomorphic to the Erdős space.
[2] Erdős space also surfaces in complex dynamics via iteration of the function
is a collection of pairwise disjoint rays (homeomorphic copies of
The set of finite endpoints is homeomorphic to Erdős space
This topology-related article is a stub.