Erdos Space and Homeomorphism Groups of Manifolds is popular PDF and ePub book, written by Jan Jakobus Dijkstra in 2010, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Erdos Space and Homeomorphism Groups of Manifolds can be Read Online from any device for your convenience.
Erdos Space and Homeomorphism Groups of Manifolds Book PDF Summary
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 one-dimensional topological manifold, then we proved in an earlier paper that H(M,D) is homeomorphic to Qω, the countable power of the space of rational numbers. In all other cases we find in this paper that H(M,D) is homeomorphic to the famed Erdős space E E, which consists of the vectors in Hilbert space l2 with rational coordinates. We obtain the second result by developing topological characterizations of Erdős space.
Detail Book of Erdos Space and Homeomorphism Groups of Manifolds PDF
- Author : Jan Jakobus Dijkstra
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821846353
- Genre : Mathematics
- Total Page : 76 pages
- Language : English
- PDF File Size : 21,9 Mb
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