Homeomorphism groups of manifolds and Erdos space
نویسندگان
چکیده
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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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 a...
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Proof. There exists an open neighborhood W of xgcb such that clsWCZ U, where els W denotes the closure of W. Let [ATjfc|fe = l, 2, • • • ] be a neighborhood base at ~1 which is closed. Moreover WEW, i.e. 4>UxEW. Thus there exists k such that ATJItCWCcls W. Hence xECk. Now from WlCU...
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ژورنال
عنوان ژورنال: Electronic Research Announcements of the American Mathematical Society
سال: 2004
ISSN: 1079-6762
DOI: 10.1090/s1079-6762-04-00127-1