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Aug 21, 2011 at 1:54 comment added John Klein Yes, I'm fully aware of that. I should have specified that K is a embedded in a locally flat way.
Aug 20, 2011 at 2:37 comment added Ben Wieland If you don't make some kind of assumption, like that $K$ is a subcomplex of a subdivision of the usual triangulation of the sphere, the addendum is not true, as the double suspension theorem gives a pathological embedding of the circle in a large sphere.
Aug 19, 2011 at 17:50 history edited John Klein CC BY-SA 3.0
edited body; added 225 characters in body
Aug 19, 2011 at 13:31 history edited John Klein CC BY-SA 3.0
edited body
Aug 19, 2011 at 13:25 history answered John Klein CC BY-SA 3.0