On separately approximately continuous functions

الملخص EN

Let Td be the density topology in R and let Tae = {A ∈ Td ; μ (A \ int (A)) = 0}, where μ is the Lebesgue measure.

We show that every separately approximately continuous (separately Tae-continuous) function ƒ : I2 → R, (where I = (0,1)) is the limit of a pointwise convergent sequence of (Td × Td)-continuous (Tae × Tae)-continuous) functions.