I was reading an article from AMM, titled,
A continuous bijection from $l_2 $ onto a subset of $l_2$ whose inverse is everywhere discontinuous.
In this he constructed the function $T:l_2\rightarrow l_1$ as $T(x)=$$(\sigma(x_1)x_1^2, \cdots,\sigma(x_i)x_i^2, \cdots )$
And shown this function to be bijective, continuous whose inverse is everywhere discontinuous.
My question is, What's the motivation behind this example? Why did the author find this example? What's the importance of this example?