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May 14, 2010 at 16:01 vote accept Igor Belegradek
May 14, 2010 at 15:08 comment added Andrew Stacey Yes, I was just being extra careful in stating the conditions. Partly because at the moment I'm thinking about how results like this generalise to things that aren't manifolds.
May 14, 2010 at 14:44 comment added Igor Belegradek Thanks! When you say ''M can be exhausted by a countable number of compact sets'' you must be thinking of non-metrizable manifolds. Any "usual" (i.e. finite dimensional smooth metrizable Hausdorff) manifold certainly has such exhaustion, e.g. the exhaustion by metric balls of any complete Riemannian metric on the manifold; the balls are compact by Hopf-Rinow
May 14, 2010 at 14:10 history answered Andrew Stacey CC BY-SA 2.5