منابع مشابه
Continuity 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 کاملAutomatic continuity for homeomorphism groups and applications
Let M be a compact manifold, possibly with boundary. We show that the group of homeomorphisms of M has the automatic continuity property : any homomorphism from Homeo(M) to any separable group is necessarily continuous. This answers a question of C. Rosendal. If N ⊂ M is a submanifold, the group of homeomorphisms of M that preserve N also has this property. Various applications of automatic con...
متن کاملAutomatic Continuity in Homeomorphism Groups of Compact 2-manifolds
We show that any homomorphism from the homeomorphism group of a compact 2-manifold, with the compact-open topology, or equivalently, with the topology of uniform convergence, into a separable topological group is automatically continuous.
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 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: Proceedings of the American Mathematical Society
سال: 1953
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1953-0060807-0