Erdős space

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 space l² 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]

References

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