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Apr 25, 2021 at 16:44 comment added Shijie Gu Maybe the boundary needs to be slightly stronger than paracompact?
Apr 25, 2021 at 14:40 comment added Stefan Friedl As stated the answer is no. You also need to assume that the image of the collaring maps is closed. Otherwise it is fairly straightforward to find counterexamples. I also spent some time trying to find a reference for this statement, but I was not successful either.
Apr 25, 2021 at 14:13 history undeleted Someone
Apr 25, 2021 at 13:52 history deleted Someone via Vote
Apr 25, 2021 at 5:59 history asked Someone CC BY-SA 4.0