About: Erdős space

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In mathematics, Erdős space is a topological space named after Paul Erdős, who described it in 1940. 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. The space is homeomorphic to in the product topology. If the set of all homeomorphisms of the Euclidean space (for ) that leave invariant the set of rational vectors is endowed with the compact-open topology, it becomes homeomorphic to the Erdős space.

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  • In mathematics, Erdős space is a topological space named after Paul Erdős, who described it in 1940. 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. The space is homeomorphic to in the product topology. If the set of all homeomorphisms of the Euclidean space (for ) that leave invariant the set of rational vectors is endowed with the compact-open topology, it becomes homeomorphic to the Erdős space. Erdős space also surfaces in complex dynamics via iteration of the function . Let denote the -fold composition of . The set of all points such that is a collection of pairwise disjoint rays (homeomorphic copies of ), each joining an endpoint in to the point at infinity. The set of finite endpoints is homeomorphic to Erdős space . (en)
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  • In mathematics, Erdős space is a topological space named after Paul Erdős, who described it in 1940. 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. The space is homeomorphic to in the product topology. If the set of all homeomorphisms of the Euclidean space (for ) that leave invariant the set of rational vectors is endowed with the compact-open topology, it becomes homeomorphic to the Erdős space. (en)
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  • Erdős space (en)
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