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Nov 19, 2012 at 22:38 comment added Jaap Eldering Indeed to confirm what @Thomas Rot said: the converse statement is not in my PhD thesis. I don't know of another place where you might find a citable reference.
Nov 19, 2012 at 19:12 vote accept ngrosse
Nov 19, 2012 at 14:12 answer added Sergei Ivanov timeline score: 8
Nov 19, 2012 at 12:33 comment added Thomas Rot I have to check, don't have time now, if the statement you want is actually in there, but a lot of these type of theorems are proven in the PhD thesis of Jaap Eldering arxiv.org/pdf/1204.1310v2.pdf . See for example Lemma 2.6
Nov 19, 2012 at 10:04 comment added Peter Michor Have a look at: MR2343536 (2008i:58001) Eichhorn, Jürgen Global analysis on open manifolds. Nova Science Publishers, Inc., New York, 2007. x+644 pp. I do not have my copy at hand, so I cannot check whether a proof is there. Since the whole book uses bounded geometry, it might be there.
Nov 18, 2012 at 23:14 history asked ngrosse CC BY-SA 3.0