If M is an oriented topological n-Manifold, is M - {x} oriented?

Question

Does removing a point from an oriented topological manifold result in a non-oriented manifold?

I know that if M - {x} is oriented, then M is oriented because we can use the two fold cover given in 3.3 of Hatcher. However, I am not able to see converse is true.

Answer 1

Yes: quote form The Manifold Atlas Project:

An open subset of an oriented topological manifold is oriented by restring the charts in the maximal oriented atlas to the intersection with the open subset.

Answer 2

No: you have this the wrong way round: removing a point from an orientable manifold can't make it unorientable (essentially because $\Bbb{R}^n$ and $\Bbb{R}^n \setminus \{0\}$ are both orientable allowing you to convert an oriented atlas for $M$ into an oriented atlas for $M\setminus \{x\}$).