# Give an example of an injective continuous map…

Give an example of an injective continuous map of $(0,1)$ to $\mathbb{R}^2$ which is not a homeomorphism onto the image of $(0,1)$.

Can anyone help me out here? This is part of a problem sheet on compactness oddly enough; yet, all I know from my notes is that a continuous, bijective map from a compact set is a homeomorphism onto the image of such a compact set.

• Not sure why this has 5 upvotes, would you say it is "well researched"? It shows no effort. Giving hints is something I encourage but upvotes should be reserved for "this person has tried" – Alec Teal Jun 7 '15 at 3:03

HINT: $\qquad\qquad\qquad\qquad$
• @Clement: No, that actually is homeomorphic to $(0,1)$. You need to make one of the loose ends approach a point on the image. – Brian M. Scott Jun 6 '15 at 17:14