Geodesic
On continuous extension of locally homeomorphic simplicial maps of $\mathbb R^2$ into itself by $\sigma$-processes
Matematičeskie zametki, Tome 59 (1996) no. 6, pp. 821-831.

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It is shown that the Klein bottle with two points removed can be embedded in the compactification of $\mathbb R^2$ by a finite tree. 
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     title = {On continuous extension of locally homeomorphic simplicial maps of $\mathbb R^2$ into itself by $\sigma$-processes},
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F. Dell Accio. On continuous extension of locally homeomorphic simplicial maps of $\mathbb R^2$ into itself by $\sigma$-processes. Matematičeskie zametki, Tome 59 (1996) no. 6, pp. 821-831. http://geodesic.mathdoc.fr/item/MZM_1996_59_6_a2/

[1] Dell' Achchio F., “Kontrprimer k odnoi gipoteze, svyazannoi s problemoi o yakobiane”, Matem. zametki, 58:3 (1995), 452–455 | MR | Zbl

[2] Tsishang Kh., Fogt E., Koldevai Kh.-D., Poverkhnosti i razryvnye gruppy, Nauka, M., 1988