What is meant by "function on the unit cube"?

Question

From these slides (emphasis mine):

We proved that any continuous function on the unit cube can be uniformly approximated by a one layer network with an arbitrary continuous sigmoidal nonlinearity.

What does the author mean by "function on the unit cube"?

Answer 1

Look at slide 8: $I_n=[0,1]^n$ is the n-dimensional unit cube.

Functions on the unit cube means functions with $I_n$ as its domain.

Answer 2

The domain of the function is the unit cube, $[0,1]^n$.