# embedding

1. ### I Injective immersion that is not a smooth embedding

Hi, I'm aware of a typical example of injective immersion that is not a topological embedding: figure 8 $\beta: (-\pi, \pi) \to \mathbb R^2$, with $\beta(t)=(\sin 2t,\sin t)$ As explained here an-injective-immersion-that-is-not-a-topological-embedding the image of $\beta$ is compact in...
2. ### I Can there be a bounded space w/o a boundary w/o embedding?

Can there be a bounded space without a boundary without embedding in a higher spatial dimension? This seems to be the kind of question I get stuck on when the big bang comes up. Thanks