English

All Parovichenko spaces may be soft-Parovichenko

General Topology 2021-10-07 v4

Abstract

It is shown that, assuming the Continuum Hypothesis, compact Hausdorff space of weight at most c\mathfrak{c} is a remainder in a soft compactification of N\mathbb{N}. We also exhibit an example of a compact space of weight 1\aleph_1 -- hence a remainder in some compactification of N\mathbb{N} -- for which it is consistent that is not the remainder in a soft compactification of N\mathbb{N}.

Keywords

Cite

@article{arxiv.1811.03912,
  title  = {All Parovichenko spaces may be soft-Parovichenko},
  author = {Alan Dow and Klaas Pieter Hart},
  journal= {arXiv preprint arXiv:1811.03912},
  year   = {2021}
}

Comments

Version 2: simpler construction, plus a remainder of $\mathbb{N}$ that is consistently not a soft remainder of $\mathbb{N}$ Version 3: new author; examples of soft-Parovichenko spaces as well as some questions Version 4: new title, corrections after referee's report

R2 v1 2026-06-23T05:10:19.358Z