All Parovichenko spaces are soft-Parovichenko
2018
It is shown that, assuming the Continuum Hypothesis, 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 $\mathbb{N}$.
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