I am preparing the notes for a course in Algebraic Topology, so I decided to borrow some of the material from the classical (and wonderful) book by G. Bredon Topology and Geometry.

Looking at the part regarding the orientation of a topological $n$-manifold $M^n$, at page 341 we find the following well-known result, with its usual proof (Proposition 7.1):

So far, so good. However, after five pages we find what follows:

This makes me confused, for at least two reasons:

**Point 1.** The Note after the statement of Proposition 7.10 does not make any sense to me. As defined, the symbol ${}_2G$ denotes the $2$-torsion part of the abelian group $G$, so if $G$ is torsion-free (for instance, if $G=\mathbf{Z}$) then ${}_2G=0$. This is clearly very different from the free-product $G \ast \mathbf{Z_2}$ (here $\ast$ seems to denote the free-product, see pages 158-159).

**Point 2.** In Corollary 7.11, take $A=\{x\}$ and $G=\mathbf{Z}$. Then, when $M$ is not orientable one finds $H_n(M, \, M-\{x\}, \, \mathbf{Z})=0$, and this contradicts Proposition 7.1, that yields the (correct, as far as I know) result $H_n(M, \, M-\{x\}, \, \mathbf{Z})= \mathbf{Z}$.

Question.Are the issues risen in Points 1, 2 above really mistakes in Bredon's book, or perhaps am I missing something trivial?

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