I need a reference on theorems unique to $\mathbb{R}$, things that go away in higher dimensions.
For example: in Topology and Groupoids, it is said that a continuous injective function $f: (a, b) \to \mathbb{R}$ is a homeomorphism to its image. I completely forgot about this fact, yet it is hugely important for gaining better intuitition for what topology of $\mathbb{R}$ is like. Does it still hold in higher dimensions? No, the 8-curve is a famous counter-example.