Erdős space

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In mathematics, Erdős space is a topological space named after Paul Erdős. Erdős space is defined as the set E of points in the Hilbert space2 of square summable sequences having all coordinates rational.

Erdős space is a totally disconnected, one-dimensional topological space. The space E is homeomorphic to the direct product E×E. Endowed with the compact-open topology, the set of all homeomorphisms of the Euclidean space Rn leaving the set Qn of vectors with rational coordinates invariant is homeomorphic to the Erdős space for n ≥ 2.[1]


  1. ^ Jan J. Dijkstra, Jan van Mill. Erdős Space and Homeomorphism Groups of Manifolds. Memoirs of the American Mathematical Society, Number 979.