T.J. Kaczynski: The set of curvilinear convergence... The set of curvilinear convergence of a continuous function defined in the interior of a cube.
T.J. Kaczynski
Proc. Amer. Math. Soc. 23:323-327.
The set of points of the unit circle at which a continuous complex-valued function in the open unit disk has limits along curves (asymptotic values) is of type F(sd) and, in general, has no other properties. The author shows that for continuous complex-valued functions defined in a cube, this set of "curvilinear convergence" does not even need to be a Borel set. He asks whether such an example can be given for real-valued functions.
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