An interesting proof of the nonexistence continuous bijection between ${\mathbb{R}}^n$ and ${\mathbb{R}}^2$ for $n\ne 2$}

Freshteh Malek, Hamed Daneshpajouh, Hamidreza Daneshpajouh +1

In this article it is shown that there is no continuous bijection from ${\mathbb{R}}^n$ onto ${\mathbb{R}}^2$ for $n\ne 2$ by an elementary method. This proof is based on showing that…