All Parovichenko spaces may be soft-Parovichenko - Dow, Alan; Hart, K.P. (Topology Proceedings, 2021)
To the memory of Phil Zenor, one of the founders of this journal Abstract. It is shown that, assuming the Continuum Hypothesis, every compact Hausdorff space of weight at most $\mathfrak{c}$ is a remainder in a soft compactification of $\mathbb{N}$. We also exhibit an example of a compact space of weight $\aleph_1-$ hence a remainder in some compactification of $\mathbb{N}$ - for which it is consistent that is not the remainder in a soft compactification of $\mathbb{N}$.