Homeomorphism groups of Sierpiński carpets and Erdős space
نویسندگان
چکیده
منابع مشابه
Homeomorphism Groups of Sierpiński Carpets and Erdős Space
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...
متن کاملHomeomorphism 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...
متن کاملNonhomogeneous distributions and optimal quantizers for Sierpiński carpets
The purpose of quantization of a probability distribution is to estimate the probability by a discrete probability with finite support. In this paper, a nonhomogeneous probability measure P on R which has support the Sierpiński carpet generated by a set of four contractive similarity mappings with equal similarity ratios has been considered . For this probability measure, the optimal sets of n-...
متن کاملContinuity and Homeomorphism Groups
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...
متن کاملHomeomorphism Groups and Metrisation of Manifolds
We prove that a manifold M is metrisable if and only if its group of homeomorphisms H (M) endowed with the compact-open topology is a qspace. We also discuss pseudo-character and tightness. All spaces under discussion are Tychonoff.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2010
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm207-1-1