Homeomorphism Groups of Sierpiński Carpets and Erdős Space
نویسنده
چکیده
Erdős space E is the ‘rational’ Hilbert space, that is the set of vectors in ` the coordinates of which are all rational. Erdős proved that E is one-dimensional and homeomorphic to its own square E × E, which makes it an important example in dimension theory. Dijkstra and van Mill found topological characterizations of E. Let M n , n ∈ N, be the n-dimensional Menger continuum in R, also known as the ndimensional Sierpiński carpet, and let D be a countable dense subset of M n . We consider the topological group H(M n+1 n , D) which consists of all autohomeomorphisms of M n that map D onto itself equipped with the compact-open topology. We show that under some appropriate conditions on D we have that H(M n , D) is homeomorphic to E for n ∈ N \ {3}.
منابع مشابه
Homeomorphism Groups of Manifolds and Erdős Space
Let M be either a topological manifold, a Hilbert cube manifold, or a Menger manifold and let D be an arbitrary countable dense subset of M . Consider the topological group H(M,D) which consists of all autohomeomorphisms of M that map D onto itself equipped with the compact-open topology. We present a complete solution to the topological classification problem for H(M,D) as follows. If M is a o...
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