In mathematics, the Erdős space is a topological subspace of the sequence space . It consists of the sequences whose elements are all rational numbers. It is named after Paul Erdős, who first described it in 1940.
The Erdős space is a totally disconnected, one-dimensional topological space. It is homeomorphic to in the product topology, and to the set of homeomorphisms of Euclidean space (for ) that fix , endowed with the compact-open topology.
The Erdős space also surfaces in complex dynamics via iteration of the function . Indeed, the set of all points such that as is a collection of pairwise disjoint rays, that is, homeomorphic copies of , each joining an endpoint in to the point at infinity. The set of finite endpoints is then homeomorphic to the Erdős space.
See also
List of topologies
References Notes
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