I need to describe a function which maps an annulus to its 'inner' circle.

Like, for mapping the torus X to the annulus Y, I said that for every point $\displaystyle x\in X$ with coordinates (i,j,k) on the torus, $\displaystyle f(X):x\rightarrow y| y_i=x_i, y_j=x_j, y_k=0$.. I'm looking for something similar to then map the ys onto a circle, by "contracting" it, as it were.