Topologizing homeomorphism groups of rim-compact spaces
نویسندگان
چکیده
منابع مشابه
On Homeomorphism Groups and the Compact-Open Topology
If X is a topological space, then we let H(X) denote the group of autohomeomorphisms of X equipped with the compact-open topology. For subsets A and B of X we define [A, B] = {h ∈ H(X) : h(A) ⊂ B}, and we recall that the topology on H(X) is generated by the subbasis SX = {[K , O] : K compact, O open in X}. If X is a compact Hausdorff space, then H(X) is a topological group, that is, composition...
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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: Topology and its Applications
سال: 2006
ISSN: 0166-8641
DOI: 10.1016/j.topol.2005.06.012