A universal continuum of weight $\aleph$

We prove that every continuum of weight $\aleph_1$ is a continuous image of the Cech-Stone-remainder $R^*$ of the real line. It follows that under  $\mathsf{CH}$ the remainder of the half line $[0,\infty)$ is universal among the continua of weight  $\mathfrak{c}$-- universal in the `mapping onto' sense.

We complement this result by showing that 1) under  $\mathsf{MA}$ every continuum of weight less than  $\mathfrak{c}$ is a continuous image of $R^*$, 2) in the Cohen model the long segment of length  $\omega_2+1$ is not a continuous image of $R^*$, and 3)  $\mathsf{PFA}$ implies that $I_u$ is not a continuous image of $R^*$, whenever $u$ is a $\mathfrak{c}$-saturated ultrafilter.

We also show that a universal continuum can be gotten from a $\mathfrak{c}$-saturated ultrafilter on $\omega$, and that it is consistent that there is no universal continuum of weight  $\mathfrak{c}$.