Geodesic
The example of the bijective mapping $f: \mathbb{R}\to\mathbb{R}$ such that $f$ is everywhere discontinuous, but an inverse of the $f$ is continuous at a countable set of points
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 4 (2011), pp. 38-39 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper we consider the example of the bijective mapping $f: \mathbb{R}\to\mathbb{R}$ such that $f$ is everywhere discontinuous, but an inverse of the $f$ is continuous at a countable set of points.
Keywords: everywhere discontinuous function, an inverse function. 
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     author = {A. Yu. Evnin},
     title = {The example of the bijective mapping $f: \mathbb{R}\to\mathbb{R}$ such that $f$ is everywhere discontinuous, but an inverse of the $f$ is continuous at a countable set of~points},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {38--39},
     year = {2011},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2011_4_a4/}
}
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A. Yu. Evnin. The example of the bijective mapping $f: \mathbb{R}\to\mathbb{R}$ such that $f$ is everywhere discontinuous, but an inverse of the $f$ is continuous at a countable set of points. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, no. 4 (2011), pp. 38-39. http://geodesic.mathdoc.fr/item/VYURM_2011_4_a4/

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