Continuity and Homeomorphism Groups
نویسنده
چکیده
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 WlCUr_i C* it follows that int U»"-! Ck9*0 and there exists k such that int Ck9£0. Let 7=int Ck and N = Nk. Then (VXN)ILCU. The proof is completed. The group $> is rigid provided that if 7 is a filter base on . It can be shown that in case X is compact the notions are equivalent.
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