Subject: Re: related question From: adamp@mimuw.edu.pl (Adam Przezdziecki) Date: Mon, 9 May 2005 06:45:16 +0200 (CEST) To: dmd1@Lehigh.EDU (Don Davis) The answer is no again. If the collection of "nice" maps is big enough to separate closed subsets (that is for each A and B closed in D there is a "nice" map f such that the closures of f(A) and f(B) are disjoint in X; this is the case for example when X contains an interval and smooth functions are "nice") then your extension property implies that the compactification B has to be homeomorphic to the Stone-\vCech compactification of D which has cardinality 2^\continuum, in particular (B,D) cannot be homeomorphic to (\bar D,D). Best Regards, Adam Przezdziecki >> >> Subject: related question >> From: Andre Henriques >> Date: Thu, 5 May 2005 23:11:28 -0400 (EDT) >> >> Here's a harder question >> related to that of Johannes Huebschmann >> whose answer I'd be interested to know: >> >> Let D be the open n-disk and \bar D be the closed n-disk. >> Let f be a 'nice' map from D to some 'nice' compact space X. >> Is there a compactification B of D such that f extends to B and >> such that the pair (B,D) is homeomorphic to the pair (\bar D,D)? >> >> Feel free to substitute 'nice' by any notion that you find convenient. >> Andre Henriques >> >> >>