/sci/ - Science & Math

I'm self-studying differential geometry from Jeffrey Lee's book (not to be confused with John Lee's book, which is also a common recommendation for the topic).

This proof for the existence of cut-off functions seems to have a small error (easily fixed), but I just want a sanity check. Clearly the support of [math]\phi[/math] is equal to the closure of O, right? And hence not contained in O.

This could be fixed by choosing r < R' < R and constructing the function using R' instead of R, but it just seems odd that he would let such an obvious error slide, especially when he doubles down on it later in the proof.